Yes, you generally get a 60-day grace period after losing your job, or until your I-94 expires if that comes sooner. During that time you can look for a new employer, file an H-1B transfer, change status, or prepare to leave the US.

I went through this last year. The important part is that the new employer must file the H-1B transfer within the 60 days. Once it’s filed, you can usually start working right away under portability rules.

If finding a job is taking longer, some people file a change of status to B-2 visitor to stay in the US longer while job hunting. It doesn’t allow you to work, but it can help you stay in status.