Drawer Runner PIece

A quick learner from Cambridge, MA says:
This was the piece not on the drawer itself, but on the front of the rail. The rail is mounted in the middle. This piece broke in half (and maybe other pieces are missing underneath the dresser itself.

I can add more photos if needed, of the drawer guide itself, or try to get a photo of a non-broken one (which is hard because I can't fully remove other drawers very easily.
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A quick learner from Cambridge, MA says:
Some additional photos of the part that is attached to the middle back of the drawer itself.

Seems to say "Kenlin" on it?
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Bob from SWISCO responded:

Thanks for posting. See our 32-081 Kenlin Drawer Socket. This could be what you're looking for. 

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