No. When your Membership expires, you will be limited to the Free to Play areas of Wizard101.
Membership allows you to rent the areas while your Membership is active. Purchasing areas with Crowns as you progress, buys those areas for access from that account, forever.
Any areas you have purchased with Crowns will still be accessible by all characters on your account who have earned entry to the area through Quest progression.
All items you earned when you were a Member that you have in your possession remain yours. Items are not removed when your Membership expires, young Wizard.