If CBP catches him, his next stop will definitely be India unless he can show CBP his travel to Romania is imminent. Though it's not like he's on a "wanted" poster, being caught would be a matter of dumb luck.
So if he wants to choose his next destination, he should make his own travel arrangements. The US has no exit controls, there's no routine stop at CBP to check your papers on exit, so they won't grab him then.
However I think your friend should talk to an immigration attorney about exactly what his situation actually is. The visa expiring doesn't necessarily mean overstay. Other countries may ask if he's overstayed, and he needs to have the Correct answer for that question, not an assumption or guess. He is expected to know, and if he gives an answer that is wrong, that is presumed to be lying/deception. Deception is serious business in immigration.
Keep in mind, also, that if he is refused entry to Romania (or I gather there aren't direct flights to Romania, so Heathrow*, Schiphol etc.), the carrier who brought him this far will be responsible for taking him away from that country to a country he is legally allowed to enter. That's not the USA, right?? That would be India, but if the airline in question doesn't go to India, that could be a big mess. And again, do they really have direct Romania-India flights? The intermediate airport must also be able to take you after what will now be a refusal. You may be better off choosing an airline that can definitely get you from the intermediate stop and Romania to India, and ideally does not require transit visas or immigration challenges for the transfer airport back to India. Emirates/Qatar/Etihad comes to mind.
* And Britain does require a transit visa, and they do ask if you have overstayed.