Depends. You'd either need the garbage collecting guy to pick up all items lying on the ground in a very large radius, or you'd need a bucketfull of garbageguys wandering around all over the place.
Yep, it's possible. But he'll either have to "pick up" (delete) the items when he comes into range (a little over a screen away), or when/if he collides (walks on) them. Or both
There's also the question of which items should he delete, and which should he leave alone? Items with movable status 2 or 3 (GM movable only or "locked down") are obvious candidates to be left alone - but what else?
Create a script that can be tagged to the beggars. They already wander around, and it makes sense for them to pick up anything they can. (having them delete it or not is arbitrary, it could be kind of fun to pick-pocket the beggars and see what trash they are collecting.)