"We don't know his life. I obviously have a background that I've created for him, but there hasn't really been anything actually confirmed by the show," DeCenzo told Collider. "We don't know who his parents are, we don't know why he is the way he is, and we don't even know his last name."
DeCenzo goes on to elaborate about what he envisions Demetri's life looks like outside of school and karate (which, again, if details are ever given, might not wind up being canon). He pictures Demetri living with just his mother, who's too busy working to intervene much in her son's life. This would explain how he manages to come home with broken noses and broken arms without ever having a parent come in to intervene on his behalf.
But DeCenzo also has a big ambition for Demetri in Season 4. "I wanna see Demetri compete in the All Valley," he said in the interview. "I wanna see him evolve his karate skills." DeCenzo says he can't yet guarantee whether or not Demetri will get that chance. Miyagi-Do merged with Lawrence's Eagle Fang dojo at the end of the show's third season. Assuming that works out, now there's a whole "Choose your Fighter" screen's worth of options for the co-senseis to pick from for the All Valley Karate Tournament.
Here's hoping Demetri makes the cut, and gives audiences a chance to see another new and different side of him: one fighting to win.