Why are you suddenly panicking and treating him like an asshole now he has anounced his resignation?
If he had ever had the intention to Do Bad Things(tm) why don't you think he also had the smarts to plan ahead and do it the day before he quit?
And also.. backing up his email in case he deletes his inbox/sentbox? Are you serious? Why don't you require that this should be deleted when he leaves? Most people do that on leaving just for their own personal security purposes. In fact many compnaies specifically require existing employees to explicitly not keep emails beyond some period. His email may well legitimately include personal stuff such as from HR that he should reasonably expect to be kept private, i.e not archived potentially permanently for perusal by IT staff anytime later.