I should clarify - legal status in the US is tied to your employment status, not necessarily to a particular employer. If they lose their job, they have 60 days to get an H1B with another employer before they start accruing illegal presence.

Also, there isn't really something called an H1B transfer. its a new H1B application every time you change your job, just that you dont go through the annual lottery if you already went through it once or have an I-140 approved.

I went through a transfer of sponsors and I can tell you that the process and cost was the same as getting my H1B the first time. The only difference was that I wasn’t restricted by the yearly cap and the transfer could happen at any time - unlike the first H1B which needs to be filed starting in April and the visa stamped in October.