You may be fired "for cause" for fallling asleep at work, and you can be fired for cause even if medication you were taking caused or contributed to you falling asleep: that is because being on medication does not justify or excuse falling asleep, and it is your obligation as an employee to not take medication that causes you to fall asleep at work (or take other steps to not fall asleep at work, such as drink coffee, make sure you had enought sleep, etc.). If fired for cause, you are ineligible for unemployment.The above is how this situation would most typically play out, but it is possible that the examiner at the unemployment division/department will feel differently: therefore, it is worthwhile for you to apply for unemployment and, if initially denied, to appeal the denial, because it is possible you might receive it--but you only might get it if you try.