Heck, I just realised that I don't think about Sonic headcanons enough to come up quickly with an answer to this question. т___т
I guess more often than anything else I think about Shadow, Rouge, and Omega becoming a "found family" and living together in Rouge's apartment somewhere in a big city. And Rouge being a very supportive older sibling figure to both of them. Like helping Shadow with clothes, makeup, dating advice...
OH! MY BIGGEST "HEADCANON" ACTUALLY IS RETCONNING SHADOW AND ROUGE WORKING FOR G.U.N. IN SONIC 06! No way they would do that after the events of SA2 and Shadow the Hedgehog x___x