STD benefits are also separate from job protection under FMLA (Family Medical Leave Act).
Starting with FMLA, I found this website that summarizes the employee job protections quite nicely:
http://fmlaonline.com/
The employer has to have 50 or more employees, and the employee has to have been at work for at least 12 months.
I am not an attorney, so maybe there is something there under the ADA provisions, but I imagine that the employer is protected under FMLA (and that would certainly be their argument if it got that far along.)
With respect to STD, you need to be employed at the time of disability to receive the benefit. But, as in cupcakespinkgal's case, benefits will typically extend past a date of termination if the person remains disabled.
There is usually some timeframe allowed to file the claim. There are cases where you know you are going to be hospitalized (like a planned surgery) where you want to file all the paperwork and get approved for the benefits in advance. However, you often have cases where you have an unplanned hospitalization/disabling event in which you need to apply for benefits after the event.
All that said, it sounds like you are still in the window of being allowed to apply for benefits. Current employment status should not effect STD elegibility/benefit.