What is visible and what is a permanent reality are not the same thing.

In the annotation, the changing body and sensations, and their object, are described as "non-existent." This does not mean that absolutely nothing exists. It means that they appear, change, and eventually lose their form, so they are not a permanent existence.

In contrast, the soul, which does not cease to exist and remains unchanged at any time, is what constitutes "reality." Those who perceive truth will discern this difference between the two. Not mistaking changes in the body for the extinction of the soul, but distinguishing between things that change and are lost, and things that do not lose their existence, forms the foundation of wisdom that transcends lamentation.

Japanese Translation from the Geeta Press Edition - Chapter 2, Section 16: "That Which Exists and That Which Does Not Exist"

In section 12 and section 13 of this chapter, the Lord demonstrated that the soul is eternal and immutable. Furthermore, in section 14, it was declared that the interaction between sensations and the mind with sensory objects is temporary and transient.

However, how the soul is eternal and how such contact is temporary has not yet been clearly explained. Therefore, in the following section, the author will define what exists and what does not exist, and show how to distinguish between them.

Sanskrit original text

नासतो विद्यते भावो नाभावो विद्यते सतः ।
उभयोरपि दृष्टोऽन्तस्त्वनयोस्तत्त्वदर्शिभिः ॥ १६ ॥

Romanization

nāsato vidyate bhāvo nābhāvo vidyate sataḥ |
ubhayor api dṛṣṭo 'ntas tv anayos tattvadarśibhiḥ || 16 ||

Things that do not exist have no existence, and things that exist will not cease to exist.

The truth of both is determined by those who seek the truth. (16)

In this section, the word "Asataḥ," meaning "non-existent things," refers to changing bodies, sensations, and their objects. It includes all material things in this objective world.

Therefore, when the master says "that which does not exist has no existence," it means that there was nothing before its supposed existence, and there will be nothing after it. Thus, even when it appears to exist, it actually does not exist.

Therefore, if Arjuna's sorrow stemmed from a fear of the destruction of Bhishma and other relatives, or any other material objects, then it was not wise to dwell on such grief.

Sataḥ, which means "that which exists," refers to the supreme spirit that is omnipresent and eternal.

The phrase "it will never cease to be" conveys the idea that, at all times and in any situation, the soul undergoes some kind of change or does not cease to exist.

The soul always remains in the same state of existence, and is constant and unchanging. Therefore, if Arjuna's sorrow stems from a fear that the souls of Bhishma and other relatives might be destroyed, then even such grief would be equally inappropriate.

The words Ubhayoḥ, meaning "both," and Anayoḥ, meaning "these," refer to the Asat and Sat mentioned above, which mean "non-existent" and "existent," respectively.

Those who distinguish between existence and non-existence, and those who perceive truth, have reached the conclusion that what changes, is subject to destruction, and does not last forever, does not exist. In other words, something that does not exist can never be said to exist. On the other hand, what always exists, regardless of time, circumstances, or any change or destruction, is existence itself. That means, something that exists will never cease to exist.

This means that those who see the truth have discerned the truth of both things that do not exist and things that do exist.