Unless you delete them, your Pieces will remain on the Newzik server, accessible by your account credentials and not by Newzik.
If you stop subscribing to Newzik, your files will still be in your account, but you will not have access to more than the authorized limit of files for a free account. Your full access will be reopen as soon as you are a subscriber again.
If you wish to stop working with Newzik, it is your responsibility to export all your content as desired to keep access to it, or at least to contact Newzik to explore the possibilities. You can also delete your content before termination if you wish.
In any case, Newzik will not have access to the content of your account even after termination.