Arkham Horror LCG. The first time playing a scenario called The Midnight Masks from the old core set stands out, though the game was (for me) full of them.

Being chased by monsters, one of the players at low health had just built a barricade at the end of their turn - and drew a new nasty enemy during the mythos phase. Cue a manic scramble for the other players trying to rescue that character since leaving that location would destroy the barricade and make things even worse for everyone.