I quit a job and got unemployment so it is possible. If you file for SS disability you'll have a better chance with a lawyer. However, if you do you may have to give up caking to prove you are disabled.

It is possible to quit a job or get fired and get unemployment. I interviewed with a company in Richardson, Texas that handled unemployment appeals for all 50 states and did training for human resource departments regarding unemployment. They told me in the interview it t was possible to get it if you quit. There were restrictions and you usually ended up going through the appeal process. Basically, an investigation was done. I am an example of being fired (for health reasons) and getting unemployment.

The whole process depends upon the company on whether or not they submit an objection when you apply for it. I have worked for companies that objected to everybody just on principal and for companies that never objected.