This isn’t a direct answer to your question because I honestly haven’t looked, but it may be relevant, I hope. I have two things that may help. Shooting paper patched .30-06, .44, and .45-70, I have never recovered a bullet that still had the patch attached. So I don’t think it stays on, but that may just be my loads. My second thing, which is probably even less helpful, is shooting cloth patched round balls out of muzzleloaders, in which the patch is usually about 10-20 feet in front of the muzzle, depending on wind conditions and who knows what else, but either way, they don’t go far. So I think it would depend on what distance our hypothetical character in the OPs novel fired his weapon from. I mean, if the muzzle is pressed against the victim, I’m sure the patch will be there, but I don’t know in what condition it will be. My ML cloth patches are all kinds of frayed at the edges, but that doesn’t translate to paper patches, I don’t think. But if the shot was taken from a distance, I would think the investigators would have to locate the spot the shot was taken from and do it quickly enough before wind, rain, etc blows away the patch or patch fragments, dissolves them in a puddle, etc.