avināśi tu tad viddhi
yena sarvam idaḿ tatam
vināśam avyayasyāsya
na kaścit kartum arhati

Translation of Bhagavad Gita 2.17

That which pervades the entire body you should know to be indestructible. No one is able to destroy that imperishable soul.

Commentary by Sri A.C. Bhaktivedanta Swami Prabhupada of Gaudiya Sampradaya:

This verse more clearly explains the real nature of the soul, which is spread all over the body. Anyone can understand what is spread all over the body: it is consciousness. Everyone is conscious of the pains and pleasures of the body in part or as a whole. This spreading of consciousness is limited within one’s own body. The pains and pleasures of one body are unknown to another. Therefore, each and every body is the embodiment of an individual soul, and the symptom of the soul’s presence is perceived as individual consciousness. This soul is described as one ten-thousandth part of the upper portion of the hair point in size. The Shvetasvatara Upanishad (5.9) confirms this:

satadha kalpitasya ca
bhago jivah vijneyah
sa canantyaya kalpate

“When the upper point of a hair is divided into one hundred parts and again each of such parts is further divided into one hundred parts, each such part is the measurement of the dimension of the spirit soul.” Similarly the same version is stated:

satamsah sadrsatmakah
jivah suksma-svarupo ’yam
sankhyatito hi cit-kanah

[Cc. Madya 19.140]

“There are innumerable particles of spiritual atoms, which are measured as one ten-thousandth of the upper portion of the hair.”

Therefore, the individual particle of spirit soul is a spiritual atom smaller than the material atoms, and such atoms are innumerable. This very small spiritual spark is the basic principle of the material body, and the influence of such a spiritual spark is spread all over the body as the influence of the active principle of some medicine spreads throughout the body. This current of the spirit soul is felt all over the body as consciousness, and that is the proof of the presence of the soul. Any layman can understand that the material body minus consciousness is a dead body, and this consciousness cannot be revived in the body by any means of material administration. Therefore, consciousness is not due to any amount of material combination, but to the spirit soul. In the Mundaka Upanishad (3.1.9) the measurement of the atomic spirit soul is further explained:

eso ’nur atma cetasa veditavyo
yasmin pranah pancadha samvivesa
pranais cittam sarvam otam prajanam
yasmin visuddhe vibhavaty esa atma

“The soul is atomic in size and can be perceived by perfect intelligence. This atomic soul is floating in the five kinds of air (prana, apana, vyana, samana and udana), is situated within the heart, and spreads its influence all over the body of the embodied living entities. When the soul is purified from the contamination of the five kinds of material air, its spiritual influence is exhibited.”

The hatha-yoga system is meant for controlling the five kinds of air encircling the pure soul by different kinds of sitting postures—not for any material profit, but for liberation of the minute soul from the entanglement of the material atmosphere.

So the constitution of the atomic soul is admitted in all Vedic literatures, and it is also actually felt in the practical experience of any sane man. Only the insane man can think of this atomic soul as all-pervading vishnu-tattva.

The influence of the atomic soul can be spread all over a particular body. According to the Mundaka Upanishad, this atomic soul is situated in the heart of every living entity, and because the measurement of the atomic soul is beyond the power of appreciation of the material scientists, some of them assert foolishly that there is no soul. The individual atomic soul is definitely there in the heart along with the Supersoul, and thus all the energies of bodily movement are emanating from this part of the body. The corpuscles which carry the oxygen from the lungs gather energy from the soul. When the soul passes away from this position, the activity of the blood, generating fusion, ceases. Medical science accepts the importance of the red corpuscles, but it cannot ascertain that the source of the energy is the soul. Medical science, however, does admit that the heart is the seat of all energies of the body.

Such atomic particles of the spirit whole are compared to the sunshine molecules. In the sunshine there are innumerable radiant molecules. Similarly, the fragmental parts of the Supreme Lord are atomic sparks of the rays of the Supreme Lord, called by the name prabha, or superior energy. So whether one follows Vedic knowledge or modern science, one cannot deny the existence of the spirit soul in the body, and the science of the soul is explicitly described in the Bhagavad-gita by the Personality of Godhead Himself.Commentary by Sri Vishvanatha Chakravarthi Thakur of Gaudiya Sampradaya:

This verse clarifies the meaning of the previous verse. Know this jiva (tat) as indestructible which is spread throughout the body (sarvam idam tatam).

“But, being spread throughout the body by its consciousness, this soul would be impermanent because it is of medium size only (being the size of the body).”

This is not so, for the Lord says, suksmanam apy aham jivah: Of small things I am the jiva”. (SB 11.16.11) As well, sruti says:

eso ‘nur atma cetasa veditavyo yasmin pranah pancadha samvivesa

One should know by the pure consciousness the small atma near which the five life airs rest. Mundaka Upanisad 3.1.9

balagra-sata-bhagasya satadha kalpitasya ca bhago jivah sa vijneyah

One should know that the jiva is the size of one ten thousandth of the tip of the hair. Svetasvatara Upanisad 5.9

aragra-matro hy aparo ‘pi drstah

The inferior soul is seen as the size of the tip of a spoke. Svetasvatara Upanisad 5.8

By these statements of sruti we understand that the jiva is very small. It has the power to spread itself throughout the whole body, just as pulverized gems or herbs when applied to the head have the power to spread their nourishing influence throughout the body. There is nothing contradictory in being small and pervading the body.

Because of its dependence on upadhis (mistaken identity), it goes to various bodies in heaven and hell. In this way the soul is also sarva gatah, going everywhere.

Dattatreya (in the form of the avadhuta brahmana) says how the Jiva, in the form of the aggregate of jivas at the beginning of creation, goes to different bodies:

tam ahus tri-guna-vyaktim srjantim visvato-mukham yasmin protam idam visvam yena samsarate puman

According to great sages, that which is the basis of the three modes of material nature and which manifests the variegated universe is called the sutra or mahat-tattva. Indeed, this universe is resting within that mahat-tattva, and due to its potency the living entity undergoes material existence. SB 11.9.20

Thus the soul’s pervasion of the body (and still being minute) is not contrary to its eternal nature stated in the previous verse. Therefore the word avyayasya is used in this verse also. It refers to the soul being eternal or nitya. As the sruti says:

nityo nityanam cetanas cetananam eko bahunam yo vidadhati kaman

The Lord is the chief eternal among all eternals (souls). He is the chief conscious entity among all conscious entities. He is-the one fulfills the needs of all others. Svetasvatara Upanisad 6.13

Or the meaning of the verse can be as follows.

The body, the jiva and the paramatma are all seen everywhere in all forms such as human and animal. The first two, the body and jiva are mentioned in the previous verse. The third, paramatma is mentioned in this verse. It is indestructible and spread, everywhere in the universe (idam). The word tu serves to distinguish paramatma from the body and jiva. The paramatma is by its very nature different from matter and the jiva.

Commentary by Sri Ramanuja of Sri Sampradaya:

2.17 Know that the self in its essential nature is imperishable. The whole of insentient matter, which is different (from the self), is pervaded by the self. Because of pervasiveness and extreme subtlety, the self cannot be destroyed; for every entity other than the self is capable of being pervaded by the self, and hence they are grosser than It. Destructive agents like weapons, water, wind, fire etc., pervade the substances to be destroyed and disintegrate them. Even hammers and such other instruments rouse wind through violent contact with the objects and thereby destroy their objects. So, the essential nature of the self being subtler than anything else, It is imperishable. (The Lord) now says that the bodies are perishable:
Commentary by Sri Sridhara Swami of Rudra Sampradaya:

The imperishable soul whose existence is a reality has been delineated and emphasised in a general manner. Now in this verse it is stated: but know that, meaning to know the reality of the eternal soul within every living entity. Pervading as the witness to the physical body which is subject to the transient modifications in the beginning known as birth and at its end is known as death. But it is not possible to modify the soul which is imperishable and impossible to destroy.
Commentary by Sri Madhvacharya of Brahma Sampradaya:

In how many ways is this to be understood? Endlessly, not limited by space, eternal, indestructible. It can not be destroyed by curses or magic and while being unable to be destroyed is also immutable.

Now begins the summation.

Thus it is stated in the Maha Varaha Purana:

Even though the soul within the physical body of every living entity is eternal and even though in all respects the use of the word tu confirms that eternity refers only to Lord Krishna alone, the temporal transmigration of bodies, feeling pain, incompleteness, these four attributes of destruction are never spoken as referring to Lord Krishna. However in relation to all other things there surely is a result in loss.

Thus is stated in the Parama Sruti:

Attributes are threefold: relating to time, relating to place and to being complete in themselves. All these attributes are residing fully only in the Supreme Lord Krishna exclusively.
Commentary by Sri Keshava Kashmiri of Kumara Sampradaya:

In this verse the Supreme Lord Krishna emphasizes the conclusive position of the soul with the word avyayasya meaning indestructible. How this is to be understood is given by the word yena meaning by which indicating the difference between the soul and the physical body which the soul pervades. This pervasiveness is so extremely subtle that it is impossible for anything to cause the destruction of its indestructible nature because whatever would be attempting to destroy it is also completely pervaded by it as well.
Commentary by Sri Adi Shankaracharya of Advaita Sampradaya:

2.17 Tu, but — this word is used for distinguishing (reality) from unreality; tat viddhi, know That; to be avinasi, indestructible, by nature not subject to destruction; what? (that) yena, by which, by which Brahman called Reality; sarvam, all; idam, this, the Universe together with space; is tatam, pervaded, as pot etc. are pervaded by space. Na kascit, none; arhati, can; kartum, bring about; vinasam, the destruction, disappearance, nonexistence; asya, of this avyayasya, of the Immutable, that which does not undergo growth and depletion. By Its very nature this Brahman called Reality does not suffer mutation, because, unlike bodies etc., It has no limbs; nor (does It suffer mutation) by (loss of something) belonging to It, because It has nothing that is Its own. Brahman surely does not suffer loss like Devadatta suffering from loss of wealth. Therefore no one can bring about the destruction of this immutable Brahman. No one, not even God Himself, can destroy his own Self, because the Self is Brahman. Besides, action with regard to one’s Self is self-contradictory. Which, again, is that ‘unreal’ that is said to change its own nature? This is being answered:
Commentary by Sri Abhinavagupta of Kaula Tantra Sampradaya:    

2.17 Avinasi etc [Here] tu is in the sense of ca ‘and’. So, ‘and’ the Soul is not of perishing nature.
Sanskrit Shloka Without Transliteration Marks:

avinasi tu tad viddhi
yena sarvam idam tatam
vinasam avyayasyasya
na kascit kartum arhati
Sanskrit to English Word for Word Meanings:

avināśi — imperishable; tu — but; tat — that; viddhi — know it; yena — by whom; sarvam — all of the body; idam — this; tatam — pervaded; vināśam — destruction; avyayasya — of the imperishable; asya — of it; na kaścit — no one; kartum — to do; arhati — is able.