It’s different for every state what they would have to do to collect on a judgment. I’m not a lawyer, so take the rest of this with a grain of salt.
From being on the other side (I sued someone who did not show up, and received a default judgment) and talking to lawyers about it, their advice was to drop it as I would spend more time and money trying to collect and may never actually see any funds. This was for about $2100, so I was surprised it wasn’t seen as worth the trouble.
In court I asked for the judgment to include my travel expenses as I had to sue the gentleman in his home state which was across the country and was told that wouldn’t be added unless it was included in a previous agreement he had signed. You may want to read your lease and see if there is anything along those lines because it could end up costing you more to ignore the situation.
You know your situation, and I’m not trying to judge, but just to share my experience from the other side, I really wish he would have at least tried to contact me and pay. I would have taken just about any arrangement, $50 a month, a couple hundred dollars a year, whatever he could do. Instead I ended up contacting law enforcement and found out he had scammed other folks as well. Instead of letting him continue, I did what I could and at that point he went to jail. I wasn’t happy about the outcome in the least for either of us.
I think @SeventhSense had some great advice regarding contacting your landlord to work something out. You may be a poor grad student now, but at some point you’ll graduate and start making some money, you’re going to want to buy a car, a house, or something. That judgment will gain interest and there may be other fees in your lease. Mine is good for 10 years, and I believe I can apply to have that extended, it won’t go away if he wants to pursue it, and spite is powerful motivation.
Good luck with the whole thing.