Between 2 rooms, there is a small single step, the step being only about 1-2 inches tall. Over this step is a piece of metal, bent in half. Mine has come undone, and has ended up broken but I've just found the same thing in another house. It looks like this:
Does this have a name? My own research gets me close with terms like "floor edge step trim" but most results I see have for flat pieces of metal, where I assume I'm after a "corner shaped" thing...!