No. In Jain philosophy, jīva does not become ajīva.

What happens is:

• Jīva = the conscious soul, living, knowing substance.
• Pudgal = matter, the physical body and material aggregates.

A living being needs a body made of pudgal to function in the worldly state, but the soul remains different from the body. The body is anupāchārya / non-self to the soul, meaning it is only associated with it due to karma.

So when a living being is alive:

• jīva is present
• pudgal body is also present
• the two are associated, but not the same

When the soul leaves the body:

• the body becomes ajīva pudgal
• the jīva does not become ajīva
• rather, the association ends

In Jain view, jīva is eternal and conscious, while ajīva is non-conscious. Because their fundamental nature is different, one does not turn into the other.

A simple way to understand it:

• A lamp needs oil and wick to burn, but the flame is not oil.
• Similarly, the soul needs bodily association in worldly life, but the soul is not the body.

So the correct Jain understanding is:

Jīva uses pudgal in embodied life, but jīva never becomes ajīva.