The silhouettes were inexpensive novelty items mainly sold at gift and novelty shops or given away as advertising promotions. They needed something as a frame so people wouldn't cut their fingers on the glass, and to give it some semblance of finished appearance. But the economics limited it to the cheapest possible frame, with the fastest possible assembly.
That was a simple "U" channel folded from sheet metal. The channel was notched so it could be folded into a rectangle. Framing of the silhouette took just seconds: wrap the channel around it or slide the glass into the loosely formed frame, then catch the hook to lock it together.
I'll suggest that the reason it was hard to identify the style is because it really didn't have one. The frames look like they were designed to be visually ignored to the extent possible.
They were never sold as standalone items, only as a component in a completed item, like a silhouette. The silhouette had a style, but the frames were basically junk serving a function on a piece of art.
A few styles might come to mind to describe the frame. For example, "minimalist" was suggested in several now-deleted answers. Minimalist is a visual style that focuses on the essential; using limited materials, neutral colors, simple forms, and avoiding excess ornamentation to achieve elegance. The frame does the first part as a result of being cheaply made, but wasn't designed or made to be elegant, and I would argue, didn't achieve it.
If it needs a style name, it seems like what would capture the essence would be something like "cheap functional" or "junk chic", but I'm not sure those are standard, recognized styles.
There are merchants selling replacement frames online. The descriptions are totally generic, like:
- metal frame
- simple metal frame
- silhouette frame (as in replacement frame for silhouette)
- vintage metal replacement frame for reverse silhouettes
There are dirt-cheap frames still made in a somewhat similar way--the simple folded sheet metal channel with notched corners. Most of the ones currently made don't require end-user bending and locking, they're completed at the factory. The metal is often embossed with some kind of design so it isn't just flat sheet metal.
They're fancier, but still generally referred to simply as "frame" or "metal frame". Finished items are typically referred to simply as "framed
<whatever>", or "
<whatever> with metal frame". The frame is non-descript so there's no description or focus on it. And since the frames were never sold on their own, they're more like a repair part for a silhouette if you want a totally authentic appearance.