ず is a classical auxiliary verb for negation, which is the equivalent to ない in Modern Japanese. And せ is the 未然形(pre -nai form) of a classical verb す, which is the equivalent to する in Modern Japanese. Thus, せず is a remnant of Classical Japanese.
Another ず example I can think of is あらず. ある doesn't have the negative from in Modern Japanese but あらず is still used mostly in set phrases or proverbs as same as せず.