'non-assignability' originates from English compounding: the prefix 'non-' (from Old English/Proto-Germanic meaning 'not') + 'assign' (from Latin 'assignare' via Old French 'assigner') + the suffix '-ability' (from Latin '-abilitas'), forming a noun denoting the quality of not being able to be assigned.

'assign' comes from Latin 'assignare' ('ad-' + 'signare' meaning 'to mark, to sign'), which passed into Old French as 'assigner' and into Middle English as 'assignen'/'assign', and the modern English 'assign' combined with 'non-' and '-ability' to produce 'non-assignability'.

Originally related to the action 'to assign' (to allot or give a share), the formation with 'non-' and '-ability' shifted the word to denote the state or quality of being incapable of assignment: 'not able to be assigned'.