What happens if a hearthstone game is unwinnable for both players?

Solution 1:

So while looking into the effects of Immunity, I found this little tidbit:

Immune effects will not prevent the game from ending automatically at the start of the 90th turn. {Hearthstone Mythbusters}

In the provided video, the two testers have Mal'Gannis on the board and continue to pass the turn to each other. Immunity is protecting both from fatigue damage, but both heroes explode on the end of the 89th turn. In reviewing notes about turns:

Each game of Hearthstone has a limit of 89 turns. At the start of the 90th turn, both heroes will explode, and the game will end in a draw. This means that Player 1 has 45 complete turns (turn 1, 3, 5... 87, 89), while Player 2 has 44 complete turns (turn 2, 4, 6... 86, 88). Player 2 does not start turn 90, he will not draw a card nor will start of turn triggers happen. This limit is very rarely reached, due to fatigue damage.

It seems to be, no matter how you have an Infinite Stalemate setup, both players can continue to play until the game forces both to "give up".