Yes, despite what an amazing number of people believe, you CAN be LEGALLY fired while on short term disability, long term disability, or any other kind of disabliity.
Collecting disability benefits offers you NO job protection whatsoever.
IF AND ONLY IF you are also on FMLA while you are collecting STD benefits, then you cannot be fired FOR ATTENDANCE REASONS until the FMLA expires; you also cannot be fired BECAUSE you applied for FMLA. However, it is the FMLA, NOT the STD benefits, that offers the job protection. In addition, being on FMLA does not provide you with any job protection for a termination that would have occurred anyway (such as the entire department being dissolved, as an extreme example).
If you want any further details, you'll have to provide additional information.