Well, if it's a US silver dollar, it has lost 4 grams in weight, which is a lot. How thick is it? Put a silver dollar in a rock tumbler and you might eventually get this.
I'll bet it used to be a silver dollar, then. The diameter of a new one is 38.1 mm. Assuming the wear is uniform, the loss of 0.43 mm in diameter also means a 0.43 mm loss in thickness. The thickness of a new silver dollar would be 2.49 mm. The volume of a new silver dollar is 2838 mm³, while the volume of yours is 2284 mm³. Since the surface of a new silver dollar isn't uniform like your is, however, the average thickness is a little less. The density of coin silver is 10.33 g/cm³ or 10.33 mg/mm³, so a new coin that's 38.1 mm in diameter and weighs 26.7 g would have a volume of 2585 mm³. I guess the bottom line is that the weight loss of 4 grams is more or less in line with what you have being a really slick silver dollar. The density of your coin would be just under 10 g/cm³, but my volume calculation assumes square rims, which is not going to be the case, so the actual volume will be slightly lower, making the density slightly higher.
Stamped metal retains BELOW IT'S SURFACE, into the molecular latticework, what is stamped thereon. Crime forensics can do a DESTRUCTIVE test with acid, that will raise a serial number, after being ground off FLAT. I'm sure there's a radiographic method that will ID the coin (if a coin). You'd probably have to know someone; I don't know if you could pay any facility - although the graders might be able to get it done for a tidy sum......
This is the premise by which Nic-a-date works. I'm not sure how well it works on silver, though. Anyone ever raise a date on a Type 1 or Type 2 SLQ?
Put it up on ebay as US Silver Dollar Basal State 1794-1935 ... I wonder how high it would go. Maybe put it in a mason jar for good measure.
with a whole bunch of Wheaties. Say: Sealed by my great-great-great-grandfather, who passed over 150 years ago.
Or try to shoehorn it into the end of a wheat cent roll and join the ranks of sellers offering "original wrapped rolls*" that just happen to have a random coin on the end. "Here is an original roll of wheaties that someone accidentally put a worn silver dollar in..." * definition open to interpretation