Permanently delete SQL server database - anti recovery
There are several ways the database could be recovered:


Database Backups. You need to make sure you're removing all database backups as well by shifting them onto on-premises storage and securely deleting on the rented server.
Server Backups. Your provider is possibly providing server-level backups. These would have older copies of the databases on them, so would need to be securely deleted.
Data Recovery on the underlying storage. The deleted files on physical storage may still be recoverable, so you need to ensure that the storage is being securely deleted. This usually involves zeroing the disks multiple times to securely delete the data.


You should check with your provider regarding guarantees for secure data deletion when you exit the service to see if that meets your requirements.