I think the second negative verb is needed if there is an additional clause, and the きり is used to mark a point in time before that clause.

There is a usage without that negative clause, though. Let me give you an example from my favorite grammar reference of all time, the 日本語文型辞典.

熱を出して子供をつききりで看病した。

Roughly, it says "I stayed with the children who had a fever and nursed (took care of) them."

In this case, it shows that the speaker stayed with the children, and didn't change that action.

Hope this helps!