prety sure

Theoretically, there is NO grace period for H1b to change the job. But there is 10 days grace period for H1b to do some sth, for example sell his car, and then leave the country.

In fact, you don't need worry about that. it's really NOT a big deal. Somebody losts his job and transfer to another in 30 days.

Another way to stay is to file Change of Status. You can fill application to change to B2 status. You will get another few months.

Take care.