If you press down on the left stick, it stays depressed. It doesn't affect the ability to actually push it down or use it, it just stays recessed deeper in the controller unless you physically pull it up again.

 

Now that I spotted it with the new Xbox Series X controller, I realise that's how it works on the old Xbox One controller I was using with my PC too. Doesn't happen with the right stick, only the left one.

 

Since it's the case on both controllers, and they both function just fine, I assume it's a feature not a fault. What's the point though?

 

EDIT: happens on both sticks, left and right, on both controllers.