In Adventure Mode: The Subspace Emissary, you can also play with two players simultaneously! Of the two, one will be the protagonist. Essentially, the camera follows the protagonist, so the other player has to keep up.
Basically, it's the same as a standard Smash brawl, so if you take damage and get knocked off the screen, you lose a life. If Player 2 gets separated from Player 1 by the screen scroll, he or she will quickly space jump back to Player 1's side. But if Player 2 gets knocked off the screen by an enemy, that counts as a lost life.