The game is Toejam & Earl. Falling off the end of a level sends you to the previous level, unless you fall through a hole in that map, then you fall to the next level, and so on.
There’s also a secret place where you can fall off in level one to go to the secret zero level.
Don’t quote me on this but I think you’re cooking! We need a name for a role that makes it easy for people to enter our industry, maybe we can call it something like entry level!