Yes it still slides but if you don't hold it ,it drops on the catch siide it's in storage but will get there to take a photo of the broken bit ...thanks..
Sounds as though is was acting as a spacer to hold the door up. If posible try and remove the door and glue it back on with a suitable adhesive. You may also be able to wedge the door up and see where it came from and glue it back into position without removing the door.