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To answer your question, I don't see why they should stop working when you have paid for the perpetual license of CS6 or for the previous version or versions. They are, and they should be, in a separate folder from the CC applications and they should remain untouched in all respect. you are using a trial version of CC right?
Hope this answers your question.
If you mean Dreamweaver CC (Cloud only version) then, no, that will stop functioning when your Cloud membership expires.
"What happens if I decide to stop my membership?
You will continue to have access to free Creative Cloud member benefits, and if you saved your work to your computer you will continue to have access to those files. You will no longer have access to the Creative Cloud desktop applications or most of the services that are components of a Creative Cloud membership."
If you mean a perpetually licensed version such as CS6 or earlier then, yes, that will continue working as normal.