Option to select a start date of a FREE membership

I have member and non-member options. Sometimes members cancel membership but there is no way for me to cancel the membership to end at the end of the billing cycle and then have it automatically start a NON-MEMBERSHIP membership option for those that do not pay a monthly rate. For any other paying membership type, the system allows a "change" in the membership to begin once the current membership is done. But the option to select a date to start a non-paying membership type does not exist.  The problem is that any member that cancels their membership become "inactive" when really we just want them going to a pay for play type member (e.g. Non-Member).