First off, a big thank you to all the kind comments on my previous post. Reading all of your thoughts helped me a lot, as I was panicking a fair amount about the future.
So, I went to my local unemployment office shortly after it all happened, but my previous company was taking a long time to send my unemployment letter to me. By the time it arrived, it was the day of my appointment. The office worker informed me the company was claiming I had quit without good reason. Which would disqualify me from unemployment income.
I told them it was a lie, to which the worker said lying on said letter was illegal, so unless I had proof of my intention to continue to work there and their intend to continue to employ me, it would be unlikely to overturn the decision. I think this worker both felt sorry for me, and nervous about me, as not many foreign residents do this process.
I asked if a signed contract by myself and the manager for the next year would suffice. Not going to lie, the worker got a little sparkle in her eye when I asked. She had me write a counter letter, stating my side of the argument.
By the next appointment, the company had miraculously changed its statement, quoting a ‘miscommunication’ between the managers and HR. I supposedly quit, but with REASONABLE cause. Still not the total truth, but this version allowed me to collect unemployment, so I left it there. I would hope that someone got in trouble for lying, but I doubt it.
Either way, I recently aced an interview for a job that offers 15％ more for the same hours with less responsibility. I'll start by the end of the month, so I've used some of this free time to have a little vacation.
TLDR：They tried to screw me out of unemployment, I proved them liars, and I got a new job.