Kull may accompany an agent, object, description or another dependent constituent. If it quantifies only a particular constituent, the scope of negation must be analyzed with reference to that constituent.
Agent: «ما جاءني القوم كلهم» concerns the complete group of those who might have come.
Object: «لم آخذ كل الدراهم» concerns the complete set of items that might have been taken.
Description or complement: kull may broaden the attribute rather than quantify the whole proposition.
Thus kull is not invariably a subject or agent. Its force is determined by the construction in which it occurs.