Thanks, everyone, for weighing in.
I probably wasn't clear...I meekly and graciously asked my former employer (who is actually a third party employment contractor who works with gov't entities) to either fill out a simple form for me including why I was no longer employed with them (I was employed with them for about 6 weeks short of 4 years at one gov't location), or to write a "separation letter" including dates of employment and reason for dismissal. I told them it was for financial purposes only, and not for a personal assessment. I sent them a copy of the form so that they could see the amount of detail they needed to provide the company and the fax number. The form referenced how I needed to have proof I was on unemployment.
The representative who was in charge of my assignment/employment said she would write the letter, but I was not allowed to view it (same with the form...I couldn't have seen that, either). I only know what it said because the financial company rep read it to me when I asked why my benefit request was denied.
The financial company already has proof that I was collecting unemployment. They said that the only way I could possibly overturn my claim is to get something from the unemployment office saying why I wasn't employed anymore. I can't just send them a copy of our NYS employment rules. Anyway, I'm afraid if I do that, it will create more issues. I'm afraid unemployment didn't check with my employer before I was granted unemployment (I don't even know how that works to be honest...our NY handbook is nebulous and looks like a kid wrote it), and that if I call them asking for proof of a reason, they'll call my employer (employment contractor), and the contractor will give them the same information that they gave the financial company. Given that the rep who signed/drafted the letter saw the form and how it referenced unemployment, I'm thinking I'm screwed.
Realistically, I can't afford to sue and it would probably cost as much as the unemployment I received thus far. I mean, right? I waited 6 months to collect due to moral reasons. The employment contractor says there is no resignation letter to them or to the gov't agency I worked for. But, there is no letter of termination, either. The only little thing I have is a couple of e-mails I sent the week I was terminated, discussing arrangements for sending my personal belongings to my house via FedEx. They never replied, which forced me to call them...and now I know why.