Recently, when I pulled up on the drawer handle a bit as usual to pull the drawer out, the entire drawer face suddenly angled oddly. Removing the drawer, I discovered that the support piece on the right side had broken loose at the back and had allowed the drawer to fall off the rails. It was being held in place with a couple of staples at each end.
Not exactly sturdy. You can see a similar staple at the near end, stretched.
Now that I'm back home, I fixed it. Seeing that there was no really good way to get screws installed into those pieces, I cut a new support piece to hold the rail up and then wood-glued & clamped a pair of gussets, one on either side, to hold everything together. Just to be safe I added a support under the left rail also. I thought about popping a couple of screws crossways to doubly-secure the gussets, but they say wood glue will hold as well as screws would.
This is the drawer with my silverware (in a bamboo silverware tray), can opener, scissors, and chef's knife. Not a huge amount of weight, but I guess it was enough to break it loose.