Can I move directly to a new job after visa cancellation or I need to leave the country?

My company is forcing me to leave the country after visa cancellation, is it required to leave the country?

I'm planning to join a new company here in Dubai during this 29 days grace period that I'll get after my visa is canceled.

But my current company forces me to leave the country and they are saying that there are some liabilities and this will be only cleared in immigration when I leave the country.

Is it required to leave the country after visa cancellation or I can switch jobs without leaving the country?