Kris,
Remember, military tactics & ability to oversee such personal items as weapons, were quite primitive compared to today standards.
The soldier was issued his weapon & was responsible for it. Whether it was the same weapon that he turned in at the end of the war, is another question.
One problem, would have been the ability to securely store weapons with an army on the move most of the time & a soldier left behind in a hospital which at most times was just a house converted to a hospital.
Usually, if a soldier was hospitalized, the weapon was stored with his personal belongings & if it was a better weapon than what another might have, it most likely was lifted.
Interestingly, there was once a research service for old guns that was available on the INTERNET. Dues to misuse of the service, it has been pulled.
But,what was of interest, was the so few weapons that could be identified by serial number to a regiment or individual.
I was one of the fortunate few that owns a Remington revolver that was issued to a bugler of the 1st MO. volunteer cavalry, who by the way, was hospitalized several times with dysentery & he still had the pistol when discharged, so yes, the weapon stayed with the soldier.
One of the most knowledgeable collector of identified civil war weapons, Wylie Sword, stated that most likely of all Civil War weapons issued, approximately 1/2 of one percent can be identified to a regiment or individual.
In response to what Jim said about regiments being issued the same type of weapon, usually, there could be a hodge podge of different types of weapons issued within a regiment. The 1st MO. cavalry had Hall rifles, (yes the cavalry did carry rifles as well as carbines at times), Sharps, 1860 Colt Armies & Remington pistols.
The army was hard pressed to get weapons out into the field so they just issued what ever they could get their hands on.
The military purchased a lot of weapons from the civilian market & a lot of 1860 Colt armies were procured as such & will not have military markings. But you can bet, if the serial number shows it was mfg. during the war period, it most likely was issued to the army.
So, in essence to Kris's questions, weapons were not tightly controlled as they are today. The army at the end of the war, did not want to own millions of weapons due to the inability to store them, & as I said, offered all soldiers the chance to buy their weapon for pennies on the dollars, but, to the common soldier who made $15.00 a month, even that was too much.