Can I go on stress leave while on suspension?

You can certainly follow your doctor's advice and go out on medical leave for stress. But that does not necessarily protect you from being terminated if the employer was going to terminate you for reasons unrelated to the medical leave. Being on medical leave does not act as some sort of shield for job protection. It only means that an employer cannot terminate the employee because of a qualified disability or, if eligible, for taking time off under the California Family Rights Act (CFRA) or Family Medical Leave Act (FMLA). If this employer was going to terminate you on Monday, it can still do so, or they can wait until you return from leave and terminate you then. If you believe that going on leave will buy you time to find another job so you can resign, that is something you can consider. Of course, the employer is not obligated to pay you for days you do not work, unless you are eligible for vacation or sick pay.