What happens if an Ice's subroutine can't be resolved?
The subroutine isn't broken (matters for stuff like Oversight AI), but doesn't actually do anything (so, technically, not "resolved", based on the unresolvable effects ruling from FAQ 1.5 - but there are no currently-released cards for which "resolved" matters).

Update: @user30903 pointed out that Persephone is coming out soonish, and will care whether a sub "resolved" or not. It seems to me that a subroutine should not be considered resolved unless it has an effect on the game state, but FFG could possibly rule to the contrary. We'll have to wait and see.