I am writing up a procedure regarding inventory that is not assigned to any specific employee of the company and would like to know if I should refer to this inventory as "non-assigned" inventory, or "un-assigned" inventory.
Non-assigned has 77k Google hits
Nonassigned has just under 8k
Un-assigned has a bit over 36k hits
and unassigned has 5.9 million and a dictionary definition
not allocated or set aside for a specific purpose
and, as a bonus, not assigned has 5.9 million hits as well
... so I think you can conclude an answer from that as to the most common usage. Unassigned would be fine.