One time during a particularly nasty battle, when half the party was unconscious and the battle could swing either way, I rolled a critical hit against the party's paladin. And worse still, I rolled almost maximum damage for the crit! The paladin only had a handful of hit points left, so this would drop him...and with only one member of the party left standing, the party was about to end up captured or worse.
So I offered the player a choice: the paladin could take the extra crit damage per the rules, and hope that the rogue could pull out a victory alone...or he could sacrifice an attuned magic item of his choice, take regular damage instead, and live to fight one more round. The player chose to sacrifice his Sentinel Shield.
He managed to stay standing for two more rounds, thanks to some lucky rolls and the Dodge action. This bought the party enough time for the rogue to feed a potion to the downed cleric, who would then cast Mass Cure Wounds and turn the tide of battle. The shattered shield ended up on the wall of their favorite tavern, still splattered with blood.
I don't do this for every battle or every critical hit, and never so frequently that the players learn to count on it. It's just something I do every now and then for the sake of drama. When used sparingly, it can make for a really cool story.