No. In Jain philosophy, ajīva cannot become jīva.

• Jīva means a living, conscious soul.
• Ajīva means non-living matter or substances without consciousness.

These two are fundamentally different categories in Jain tattva. A soul is eternal and never turns into matter, and matter never becomes a soul. What can happen is that jīva and ajīva come into contact through karma, but their essential nature does not change.

In simple words:

• Jīva remains jīva
• Ajīva remains ajīva

This distinction is very important in Jain darshan.