Probably Jotaro gave them to Star
Why did Jotaro gave his pants to a ghost is the real question.

Fuck it, I'll give it a shot. Making sense of Araki's inconsistencies gives me life.

So stands are the manifestation of their user's spirit, and we clearly see that some stand can change appearance to match their own user's current state or whatever. Star Platinum got a wardrobe change (slightly longer boots that cover the legs) in between parts possibly because of an inner change that Jotaro went through that would have altered his spirit and new general attitude. He also understood Star Platinum's abilities better once he gained the time stop before Star Platinum changed clothes.

I bring all that up because when Star Platinum first manifested, Jotaro had no idea what it was exactly, nor did he fully control the stand at that point as he demonstrates. Once Avdol and Joseph go on explaining just what's going on to him, he fully acknowledges Star Platinum as his stand, and it takes a form more independent of Jotaro's own appearance; he loses the pants and gains his little tiara thing.