The answer to your original question is yes, there probably is a record of who substituted for your relative. It's going to be hard to find, though. My wife had a relative from Tazewell Co. who was listed on the draft rolls and became a "d&s", which stood for drafted and substitute. His name was Jurgen Heits Freerks. I found out his name morphed to George Freak and in 1864 he joined the 45th Illinois. Several places in his records it says he substituted for John McJilton, who was a farmer with 4 young children from near Olio, Woodford County. I saw the name several times in Freak's service records, which I obtained from the National Archives, and in the Illinois Civil War database. I believe the Illinois database was taken from the original muster rolls.
I got the draft rolls from ancestry.com by signing up for a two-week free membership.
It might take a lot of work to look it up but like I said there probably is a record of it. Local newspapers might also be a source.