[dudul]

I used to be on a H1B and changed employer 3 times, I'm well aware that it is possible.

But having a H1B comes with a stigma, not all companies are willing to get involved with a new petition.

And let's burst the myth of the "grace period", it doesn't exist. If you're fired you have literally 24 hours to leave the country. There is no "2 week grace period" to find a new employer. So yes, it is possible to find a new job, but it makes it very difficult to fight back when you're asked to work nights/weekends for example.