I played a game recently where you have the opportunity to investigate a murder. Every time you sleep without having solved it, another NPC gets killed. Initially, they are fairly inconsequential (them dying feels bad, because may have spoken to them and now you let them down, but they aren't integral to the story), but eventually a vendor gets killed, which means they aren't around for you to buy things from.
It's not critical if you don't solve the case; there's very minimal mechanical impact to just walking away. But it's a nice way to add some pressure and make the world feel more alive.
