continued use of software after membership expires

From the Creative Cloud FAQ here http://www.adobe.com/products/creativecloud/faq.edu.html under the General information section:

If I decide to stop my membership, will I still be able to use my Creative Suite software and the other components of Creative Cloud?

When you cancel a month-to-month or annual membership purchased directly from Adobe or let a 3- or 12-month prepaid membership purchased from a retailer expire, you will no longer have access to the CS applications, other desktop software, and services that are components of Creative Cloud. However, if you saved your work to your computer, you will continue to have access to those files. You will also have access to the same benefits as a free Creative Cloud member, which include 2GB of storage space (reduced from 20GB), the ability to sync and store your files, access to a free 30-day trial of the desktop software that has not already been installed and provisioned as part of your paid membership, and access to the free level of services included with Creative Cloud.

Not the Cloud apps, no. You never own them. You perpetually lease/rent the right to run them.

Anything you owned prior to joining the Cloud will continue to work. Any Cloud apps (CS6) will cease to work.

You keep whatever work you've created using the software but you will lose the use of the Cloud software until you either a) re-join the Cloud or, b) purchase a perpetual license.