[servicepub (RIP)]

Identity discs only make it home when the wearer does. When a soldier dies one disc is removed and makes its way to the Adjutant while the other remains with the body.
Typically, a body will be left behind during the actual fighting. Immediateely afterwards the body may receive a quick, shallow burial - more for sanitary reasons than for any other. The spot is marked for the Graves Regsitration Unit (a US Army term but I can't remember the Cdn term) to recover the body and move it to a more permanent spot. The ID Disc that remained with the body helps ensure that the right wooden marker is properly matched. Later again, the War Graves people come along and move the body to its final resting place. Again, the disc is referred to.
Meanwhile, the adjutant has used the disc that has been turned in to start the official paperwork required by the army. There is no requirement to retain the disc afterwards and I have never heard of anyone who wished to collect these as souvenirs during the war.
Nowadays ID Discs are highly collectible, especially as many units can be identified by these discs.