The "Final Egg" referred to by QoiZ is Sonic's 10th action stage in Sonic Adventure. There are a lot of Final Egg glitches, so it helps to be specific, but I know which one is being referred to here. Upon emerging from the start of area 3, turn around and jump into the void (after setting Free Camera, something you can only do on the GameCube version). If you jump far enough, you don't die; instead you go freefalling through a void. If you navigated the right way, after about 8 seconds of falling, you'll land in a hallway that drops you off near the end, skipping most of area 3.
I'm actually reminded of the Dreamcast-only ending to Eternal Engine on SA2 more so than Final Egg, but the tie to Defection is pretty much the same.