Cockroaches can live for about a week after they lose their head.
Mulder and Scully find Leonard Betts' decapitated head disposed in a watery tank of biological waste. Scully explains that the organic waste will be sterilized with microwaves and ground up for safe and easy disposal. Yes, believe it or not, this is an actual process. The technologies and procedures for microwave incineration were developed at NASA's Ames Research Center, and as far as I know, are not yet in widespread use. While Mulder decides to search for clues in Leonard Betts' apartment, Scully prepares the head for autopsy.