rec letter required after previous Residence Permit is canceled?

Situation:
I'm in Suzhou. I got terminated by a school, though they want me to sign a resignation letter. I haven't signed anything. But let's suppose the Foreign Expert Certificate and Residence Permit are canceled shortly. I find another school that wants to hire me, either when I am on a 30 day stay permit, or on a tourist visa after exiting/re-entering.

Can a new foreign expert certificate be issued to me without the recommendation letter from the previous school?

If the answer is no, are there any exceptions to this? Is a recommendation letter from a different previous Chinese employer acceptable?

What if I won a settlement or a labor arbitration hearing for illegal termination or other violations of my contract and/or contract law?

It doesn't seem reasonable that one company could determine a person's ability to work in China for the rest of eternity.