H-1B holders generally have a 60-day grace period after termination to find a new employer, change status, or leave the U.S. This grace period applies only once per validity period.

If another employer files an H-1B transfer within those 60 days, you can usually stay and begin work once the petition is filed. Timing is important, so act quickly.

I went through this last year. I used the grace period to consult a lawyer and change to a visitor status temporarily. Planning early makes a big difference.