Listings not going into draft status once expired and overdue.

Recurring listings with a free trial period, need to be signed up at PayPal.
If the user does not subscribe at PayPal the listing stays in draft.
If the user does subscribe at PayPal [but does not pay yet because of the free trial] an IPN notification should set the extended [if paid] or draft [if not paid].
If nothing happens, that suggests that there never was a subscription.

If, like Kiran says, the original invoice is not paid, then there is no subscription activated.
Even a subscription with a free trial will generate an original paid invoice.

Was the listing generated from the frontend by admin or another user?
Is there a PayPal subscription for the listing in your PayPal account?

Thanks

Was the listing generated from the frontend by admin or another user?
Is there a PayPal subscription for the listing in your PayPal account?

If there is no contract at PayPal, then there is nothing to cancel.
Being a registered user on your site has nothing to do with a user agreeing with PayPal that PayPal can pay you every month.
It does not matter if there is a free period or not. If set up as part of the recurring package settings, then the user needs to enter into the PayPal contract on the same day as the free package starts. The first payment only is taken out of the user’s PayPal if the free period is finished and the contract is in place.

Changing or adding listings from the backend has no effect at all on PayPal. Only creating a listing from the frontend can create a contract if the user completes and agrees to the contract.