No, but you can go on short-term (or long-term) disability at many companies. There's an unfortunate pooling of sick time/personal time/vacation time at many companies today. But, in the US, it used to be absolutely the norm to have separate PTO and sick days and you were only expected to use the sick days if you were sick. (And they typically didn't roll over.)

And, if you left for whatever reason, you were paid out your accrued PTO (which often had an accrual cap) but not sick time.