bathroomcabinetsdoors
My bathroom has a white cabinet, where one of the doors has an adhesive rubber strip running down the inside of the door.
This is so when both doors are closed, you cant see a big black gap in the space where the door edges meet.
I need to replace one of them, as it has shattered, but Ive no idea what to search for? Do these little babies have a name?
You're looking for a Door Shoe
A Door Sweep
Or a Threshold with a vinyl seal
Or a combination of these.
These products are typically used to weather seal an exterior door from the elements, but should work just as well in your situation. They should all be available at your local home improvement store.
Based on your excellent diagram, I think these may be your ticket. They are designed for your very problem.
Disclaimer: I've never bought anything from the site in the link and I'm not endorsing them.
Best Answer
I would probably call it a back plate, a span strip or a draft blocker.
I would probably be wrong, but that's what I would call them. I've never shopped for one on their own, I usually fabricate such things out of strips of hobby wood.