Since most guns taken are associated with felony charges, they will be sent through each county's Circuit Court. All major felony cases go through here, no matter if they are city PD, county SO, university, or other cases. Since the Sheriff is the Chief LEO of the county, and the LE agency associated with Circuit court security, the duty to dispose of seized items falls upon him, or his designee.
If they don't destroy them, they are usually "auctioned" to local FFLs. However, this is rare since most agencies tend to hang on to their evidence due to appeals, which can drag on for years. Think about that crackhead on death row, who is still appealing his murder convictions from the 1980's. Since a new trial could be ordered at any time up until his execution, the evidence must be retained.
I have personally performed a routine catalog of firearms in evidence at my old PD that were first entered before I was born. Some are still from cases on appeal. Others just haven't been disposed of. Since it's not illegal for them to just sit there, it's often not a top priority for an agency to dispose of them.