Unless some effect intervenes, this will result in them burning out repeatedly, giving 1 point to an opponent each time, until an opponent passes the Victory Score and wins the game.
§ 431.3.a Core Rules PDF (officieel)
§ 431 Burn Out
§ 431.3 A player's Main Deck may remain empty as they Burn Out, usually because their trash is also empty. When they attempt to perform the original action again, it will cause another Burn Out.