Your software will stop working when you stop paying for it.
Your website hosted on a commercial, 3rd party web server will not go away. But you will need to use an FTP Client (Filezilla.org) and HTML editor (Brackets, etc...) to edit and maintain it.
If your site is hosted on one of Adobe's hosting products (Behance, Business Catalyst or ProSites) then it will disappear from the radar. Obviously, that's something to consider when choosing a host.
Nancy O.