In my city, they had a drive like this. a relative of mine said that everyone dropping off a gun a secretly photographed and the guns were checked to see if they were stolen and tested.
Also,I have heard rumors that war prizes were taken by officers in some depts. But then again, that is a rumor. I hated to see the TV reports of people dropping off Lugars and P38 or a colt 45....
I suspect any decent gun goes home with a cop.