It's a Winchester "Supplemental Chamber". Can't tell if this one is .30-30, .30-40, or .32 WS. WW made them for indoor/gallery use. Most likely it will accept a .32 S&W (the original short version) or .32 Colt (if a .32).
Neat find. No idea on value.
Bingo. Kind of common a generation or three ago. Not so commonly found today. Collector's value in the $50 range, if it's pristine, which this one isn't. Looks like either a .30-30 or .303 Savage- it should say in the small print on it. Yeah, intended for shooting .32 S&W in the parent gun, either short or long- sometimes marked for such, sometimes not, drop a cartridge in and see if the long sticks out. They exist for .22 centerfires ( to shoot .22 RF's), .25 centerfires (to shoot .25 RF's) via self contained firing pins which detonate the rimfire cartridge when impinged upon by the centerfire rifle's firing pin. I wouldn't be surprised to learn they exist for larger calibers too- but if they do i haven't seen any.
I went on a binge seeking these things out a few years ago and acquired a bunch of them. Long story short, they don't really work worth a tinker's dam. Oh, they go bang, but don't expect great accuracy out of them. If you need to shoot a chicken from across the room with a .32 pistol bullet out of a .30 rifle it'll do the job but that's about it. Maybe an empty beer can at 20 paces. Maybe. At least in my experience.
I'm now secure knowing I have a dozen or more different ones in a drawer in case of an apocalypse wherein I'll run out of rifle ammo and have to resort to using pistol ammo of which I have little of that flavor. But seriously, one of these plus a couple .32 cartridges in the pocket would be just the ticket for administering coup de grace shots on a wounded hoofed animal, if one was of a mind to fumble the adapter out, load it with a .32, insert same into the rifle, and proceed with the deed.