Only to someone else willing to sponsor them, and timelines can be tight. I might have over exaggerated with “no mobility” but it is frequently shown that their employment status is used to control.
Obama admin during their lame duck days introduced a one time grace period(within 3 years) of 60 days. If you lose that new job, you're supposed to leave immediately. However, immigration officers usually waive minor periods of unlawful stay before filing for a transfer, how many days is a matter of your luck.
>And your employer possibly requires you reimburse them for all sponsorship fees
This is pretty illegal and even the shady body shops never do this.
Also the law states that that company has to reimburse the employee for the return tickets.
The real problem with the H1B system IMO is the uncertainty and inconsistency of everything which leaves those affected in a constant state of concern.
When I was on H1B and faced that situation, I talked to an immigration attorney who told me how things really work.
Caveat: This was 10+ years ago. I doubt it's changed, but talk to a lawyer if you're concerned. A one hour consultation won't break anyone's finances.
Like I said, talk to a lawyer if you want to know what's really up.