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 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.