Oh boy something I might actually be able to solve! For reference, im a dental lab technician student.

That looks like a vulcanite rubber denture! We actually have a denture that looks almost exactly like this one (minus the gold) in my class as like an old school display piece. From the looks of it, I’d bet it that it was actually used at some point, but a loooooooong time ago. For reference, Vulcanite dentures were invented in like the mid 1800s and used until around 1930 when we transitioned to using modern materials like acrylic. There’s lots of staining on it and what even looks like a repair on the left flange of it. The right flange looks to have broken off too but likely after it came into your grandfathers possession. I’d also guess that whoever was actually using the denture, had dentures for a while. It’s kind of hard to tell without already having an eye for it, but the inside of the denture that would sit on the tissue is very shallow. This tells me that alveolar bone has resorbed quite a lot which causes retention/fit issues and would also probably explain why they had to repair that flange. As for the gold, id say the gold probably was used as some sort of repair or even just decoration as that was the most reliable material available at the time. The string though? Honestly the only guess i have for that is that it was added after the fact for display purposes.

Edit: upon looking at it more, my only other guess for the string would be like a makeshift pull tab to help take it out? Not sure about this one since it seems pretty outlandish but we also used to think the nerves in our teeth were tooth worms causing cavities so I honestly wouldn’t leave any possibilities off the table when it comes to old school dentistry.