Board Game Arena

It happened in one of my arena games.
Someone got kicked because of inactivity and another left without getting a penalty.
But they receive the first card:
1: Why? It just make for other players that we know the cards
2: I wonder what happens if they get an action card, the game is frozen for eternity ?

Once a player quits or is expelled, the game is left in a broken state. For some games you can continue the fiction of playing, but other games may fail or get stuck in different ways. In any case, whether or not you continue, the result is already decided: the player who left lost, and everyone else tied.