Can a company that asked you to resign keep you listed as employed, so its not possible for you to get assistance?

I was asked to resign from the company i worked for in April after 2 weeks I tried to sign up for assistance, since I have a child he needs insurance and foodstamps temporarally but was told I am still listed as employed. My case worker gave me a paper to have the company filled out, I emailed it to them and they called my worker and told her that they would not fill it out and that I was awaiting suspention( which is not true, they gave me the option to resign or be terminated) what can I do? I just need to be able to feed and insure my child