TRACON Controller reported an aircraft experienced a generator problem resulting in lost communications and no transponder. The aircraft flew below the Minimum Vectoring Altitude while diverting to a nearby airport.

Narrative

Aircraft X was climbing for victor airway to 130. Shortly after leveling at FL130; they gave a radio check and stated they had a generator issue. I asked them if they wanted to continue or return to land and they said continue with no emergency. I coordinated with ZZZ Center and as I finished Aircraft X chose to return to ZZZ Airport. I cleared them to ZZZ Airport via radar vectors 290 and descended them to 11;000 ft. I quickly advised ZZZ Center of their return and quickly Aircraft X transponder dropped. I quickly tried to reach out for radio and they were already gone from frequency. They continued for about 10 miles and made a couple of turns. They then headed east and dropped off radar. I had already advised ZZZ1 Tower of their possible divert. I attempted to reach out on guard; etc. several times. I asked tower to try to reach Company. All of our LOAs and contact information are incorrect; we were unable to get a good contact. I advised both bordering ZZZ Center sectors to protect. The pilot eventually was able to land safely at ZZZ1 after our supervisor eventually was able to text message the pilot who also experienced a gear issue. I have no idea what to recommend. There isn't much you can do when you lose communications on an aircraft. I wish I wouldn't have descended to 11;000 ft. as promptly; pointed at a 12;700 ft. and 11;500 ft. MVA; but I had them in the face of departures and wanted to ensure I could top them with those departures. I guess I did what I thought was right and ended up worried when the worst happened.