Against the Storm (and excellent rouguelite city-builder) does this in a really cool way. Pausing is a core mechanic of the game, and you frequently pause while you place building or things like that - and all the visual animations stop (fire, rain, trees swaying, etc).

But when you find a broken ancient seal in the forest, the giant creepy eyeball moving around in it keeps moving even when you pause the game, which helps emphasise how other-worldly it is.