The owner and the managers can do it, with Remove project in the ... menu of the project's row or the red Remove project button in the Delete project section of Project settings, and SyncNow first lists exactly what is removed and kept and asks to confirm. The project is removed for everyone: when a manager removes it, the owner loses it too but stays its owner and can add it back.
Removed: the FTP and MySQL credentials, from the SyncNow vault and from the PC; the project's settings on every PC of your account; the managers' access, with an email to each of them (and to the owner, when a manager removes it), while pending invitations stop working; the project's agent work counters and SyncNow's own control files on the PC. The only file SyncNow removes from the hosting is its own database gateway, if it installed one.
Kept: the site, any local files SyncNow did not create, and the Activity history as a record of the work done. Removing cannot be undone: to work on the site again, add it back and enter its credentials.