If this is happening in the U.S., then the employee is probably an "at-will" employee, who can be fired for any reason whatsoever - as long as you're not discriminating against him based on his sex, religion, or membership in some other legally protected class. People who've slept with your wife are not a protected class under law.

The point is giving an employee nothing useful to do so that they resign may be the same as terminating them, so they might still be entitled to severance or unemployment benefits.