If *all* the requirements are met for FMLA, then you can request job protected leave under FMLA. It offers up to 12 weeks of job protected leave.
However, to answer your question, you can be terminated while on disability leave if you have no type of job protection under FMLA or ADA....Disability income is just income you get while on leave but does not protect your job (FMLA does that).
Also, I might mention that even under FMLA you can be terminated if you would also have been terminated had you not applied for/been on FMLA (such as your job is eliminated while on FMLA & it would also have been eliminated if you had not been on FMLA).