The workshop is called something like "Garbage Burner". It needs some fuel, obviously, but the items should also count as fuel. So you need some fuel to get it started, but when you load it with socks or whatever, they count as fuel as well so it won't use a lot of fuel.
How it works: You can mark items with a b for "burn." Items markes such creates a hauling job where the dwarf carries the item to the Garbage Burner. A job then is created to "burn item", and when the job is done the item will be deleted.
The goal is to make it easier to get rid of unwanted items without having to do tedious manual clicking of dump them and then pull levers to atom smash them.
It should be possible to set item types to auto-deletion such as xsockx. The player should be able to select to auto-destroy items of x, xx, xxx or not as desired. Same with rotten items and body parts. There should be a screen somewhat like the stocks screen where you can select types of items for auto-destruction or not as desired.
The Garbage Burner workshop should not be able to destroy items made of stone and metal but everything else it should be.
If desired it can create an item "Dirty ashes" / 20 items burned which maybe can be used to create low quality fertilizer.
Stark raving mad dwarves are liable to rip the clothes of a random dwarves and burn them as garbage as well as pick up random wooden furniture and do the same.