Can my friend return to the U.S. after voluntary deportation?

The answer is probably yes. But keep a few things in mind. First, getting back to the US generally requires a visa. Qualifying for a visa may be as difficult to do in this situation as ithe issue of your friend having remained here without authorization. Second, your friend's arrest may likewise create a problem obtaining visa issuance. Third, a common misconception is that someone who leaves the US after having been granted voluntary departure can immediately turn around and apply to return as if no violation of that individual's immigration status has occurred. Not true. Yes, leavind under an order of voluntary departure may avoid SOME problems trying to return, the fact is that anyone who leaves after having remained here in violation of US immigration law is unlikely return without a fight. My advice would be to consult with a competent attorney and become informed. Be careful out there. Good luck.

It depends on what the reasons were for his having to leave and what the conditions of his vol. dep. were. If he tries to return, he has to have a basis on which to return (an immigrant visa petition, a non-immigrant visa petition) and that would have to be approved and he would have to either have satisfied the conditions of the voluntary departure or get a waiver of those conditions.

Your friend may come back to the U.S. if he has a legal way in which to do so. He will need to be a beneficiary of an employment based or family based petition or apply for a tourist visa. He must have authorization to re-enter the United States. With voluntary departure he simply avoided having a removal order on his record and being barred from re-entering for 10 years.