Find Memberships with no auto-renew

The Find Memberships search only returns memberships that have no recur contribution id (== NULL) when searching for no auto-renew memberships. We have a situation where several memberships have a recur contribution id but the contribution has been ended (end date is not NULL). When you view these memberships the auto-renew is not checked. This doesn't seem to be an accurate result when all you search for is no auto renew.

I am ready to fix this but I have questions. Should the recur contribution id be NULLed in the membership when the auto-renew is ended or should the search check if the recur contribution has been cancelled/ended? Or was the search supposed to only return the memberships with no recur contribution? The current code doesn't seem to do anything except enter the date when it's cancelled.

This site is using Authorize.net. I believe the scenario was that the auto-renew was cancelled in Civi first, resulting in the subscription in Authorize.net being cancelled.

An accurate list of memberships without a subscription is vital to our client so they can know when their customers have stopped paying for their product.