The green card process is not transferable. Once its started the applicant is stuck. I personally saw the company slow roll the process for one of my directs. I kept hassling them to move it along but to no avail. I saw this happen to colleagues at numerous companies.
It is transferable under AC21. But that’s not the point. You are not stuck with an employer on H1B.
Yup. I had a star developer on my team that we had been planning to sponsor but the company was being sold and our future was unclear. I had to advise her to go find a new job, because if she started the process with us and got laid off, even finding a new job willing to sponsor, she'd have to start over. She would run out of time on her existing visa and lose her legal status altogether.