When an item is marked "a", it is no longer property of the state; anyone can take it and do with it as they choose, gaining official ownership of the item. If no one takes possession of the item, it next time there is a job sweep, a second sweep will be conducted (so as not to employ employed dwarves) to take an "a" marked item to a new workshop call the public warehouse. This workshop has no jobs associated, but any item placed in it, whether normally stackable or not, will be treated as a stack with items of the same quality and material, with exemptions for decorated items and bolts. Craftable items (rocks and such) could be claimed by dwarves on break to make themselves some kind of craft or piece of furniture; they could either do this from their rooms, or perhaps in workshops whose base material has been marked "a". If they made furniture, they would set it up in their rooms, increasing value and giving good thoughts ("Urist mcCrafty feels good about having made his own furniture") Little baubles they make could either be kept, worn if jewelery, or given to a friend, lover, or potential lover. Perhaps culture could come into it, with marrying dwarves having to make each other an amulet before spores can be exchanged, or enemies making each other figurines of the others horrible death at the hands of a cavy.
This system would have several advantages. One, it would give us an alternative do atom smashing or lava dumping or other such behavior; instead of tracking 1000 sandstone units, it tracks one 1000 stack of sandstone (less if quantum stockpiles are ever fixed), none of which are tracked as anything more than a single number associated with that workshop. Two, it would give a little personality to the dwarves, with them customizing their rooms and exchanging little gifts and some such. Three, it would allow you to control what dwarves do and don't claim; No more dwarves charging onto the battlefield to grab their rightful left sock (standing order that locally produced clothing is claimable by default). Fourth, it allows you to arm civilians who would be willing to fight, with the brave and reckless helping themselves to your weapon-smith training fodder.