The Falcon flew into the engine bell, but the other footage we see from further into the chase, they're flying alongside the massive cylinder of the engine, in a gap between it and its mountings in the ship's infrastructure. There's probably a hole somewhere...
--Jonah
I'm assuming, for my own nitpicky sanity, that the ship was probably gutted of anything useful after it crashed. No sane pilot would fly into something they didn't know they could maneuver in.