A few months back, the 13-tooth sprocket on my Tour Easy started skipping, which reminded me that I planned to replace all the drivetrain components. Time passed, the winter remained unseasonably warm and sunny, we kept riding, the skipping got much worse, and I just shifted across that sprocket.
Finally, the rains returned, I heaved the bike up on the workstand, and started replacing things. Judging from the accumulated crud and severe wear, it’s been on there for quite a while:

Here’s the offending 13-tooth sprocket, all shined up;

I don’t recall a catastrophic failure that stripped all those teeth off in one shot. A closer look showed cracks in the few remaining teeth:

Which explains why the skipping gradually got worse: the poor sprocket shed teeth as I rode blithely along.
Huh.
That’s what happens with a severely worn sprocket: the chain applies tension to just the topmost tooth, rather than distributing it on the teeth around a third (or more) of the sprocket, and, one by one, that force breaks the teeth. The top picture shows at least one other sprocket with a missing tooth; all display the shark-fin profile of heavy wear.
As you can tell from the other bike pix & repairs around here, I’d rather ride than mess around with cleaning and suchlike. We’re on our second set of drivetrain components in 15 years, so I’d say treating all that stuff as consumable seems a fair tradeoff…