Cancel Membership Expiration

By default, when a user cancels their membership on your site running Paid Memberships Pro, their membership is revoked immediately and they will no longer have access to membership content.

This is usually what you want. We advise our users that usually when someone cancels a membership on your site, they don’t want anything to do with you anymore.

there is some code to change PMPro cancellations to cancel the subscription, but leave members with their level until their next payment date.

Unfortunately this code is for paid members of PMPro
http://www.paidmembershipspro.com/change-pmpro-membership-cancellation-to-set-expiration-date-for-next-payment-instead-of-cancelling-immediately/
You might be able to find it elsewhere on the net.