Re: @Arthur the cat ... This isn't that unusual in the U.S.
If you don't sign the new agreement, you're gone.
You live in the US, land of the corporate lawyer and no employment rights. Here firing someone for not signing a new contract would be constructive dismissal which would cost them dearly.
Also, at the time all software companies in the area had major problems finding staff, which meant that a) getting a bad reputation for mistreating staff was a total no-no, b) I could have got a new job with a couple of phone calls, and anyway c) I was essential enough to the company that the local UK management would have flatly refused to fire me.
As to the lawsuit. That was predictable. Because you worked for them and are now creating a competing product?
Nope, not a competing product. They'd canned the project because "it wasn't core software". We moved into an area they weren't in. A few years later when we were succesful they did want to be in that area - so they came to us asking nicely for a partnership.
(Yes, it sucks, welcome to America where lawyers can be found under any rock... )
Which is why I'd turned down a couple of US job offers a few years before and remained in the UK. I think you missed that I originally said "When I worked for the UK subsidiary of a US corporation"?