I’m not sure if I’ve ever heard of such a case and I used to be into taxonomy a bit, though no expert. It’s certainly possible, because stranger things have happened in museum science. But I haven’t heard of any in that exact category. If it did, I might bet on some obscure arthropod being most likely (and easiest to elude discovery).
If such a critter did exist, especially in the good old days, it likely would just be re-assigned it’s own species name and a holotype for that single critter based on distinct coloration/gross morphology and which would then be presumed extinct. Museums are almost always tight on cash and recovery of genetic material from a random 250 year-old taxidermy specimen living in a drawer is not going to be a high priority. It would almost certainly languish until some curator or outside grad student doing a very specific study on closely related taxa came wandering through with an outside research grant. Which means discovering such an oddity is a statistical long-shot. Might happen eventually, but what eventually means in that context is anyone’s guess.
Holotypes are reassigned and museum specimens synonymized all the time. Historically, anyway. Especially as fallout from the great boom of the 19th century gentleman naturalists, when an awful lot of animals ended up being described from dead specimens collected on expeditions. Which could lead to some weird screw-ups.
Over in the ‘Today in nature I saw’ thread I posted and commented sarcastically on a series of photos I took of a pair of ring-necked ducks. The glossy, reflective ring around the neck of the adult males is apparently super-obvious and stands out when when you have a dead duck in your hands. In the field it is usually virtually impossible to see unless the light and angle is dead perfect. Leading to generations of inexperienced birders blinking in confusion as they try to find a hidden ring.