Your son is already suffering the consequences of his wrong decision, and I have no doubt he's going through a very difficult time. I don't know the full situation, of course, but if you were in his shoes, wouldn't you hope your parents would help you heal from this experience instead of rebuking you or turning you away? After all, your son doesn't just need a place to live; he also needs emotional support -- a place where he knows he'll be loved and encouraged during a very hard time in his life. You should be honored that he believes he'll find it by returning home.
At the same time, it's important for you to remember that your son is an adult now, and if he does come to live with you for a time, you need to respect this. It's not always easy for parents to deal with their adult children; ask God to give you wisdom. Remember what the Bible says: "Live in harmony with one another; be sympathetic, love as brothers, be compassionate and humble" (1 Peter 3:8).
Most of all, pray for your son, and urge him to turn his life and his future over to Jesus Christ. God can take even the hard times in our lives and use them to draw us closer to Himself.