In Google Drive, only the owner of the file or folder could delete them [1]. Users with edit access to folders could add and remove files from that folder.
By the other hand, users will be the owner of the files and folders created by them until they transfer the ownership to another account. To learn how to transfer the ownership of a file see [2].
It's worth to say that as a Google Apps administrator [3]...
You can restore deleted Google Drive files or Gmail messages for one
or more users for a date range you specify. This helps ensure that, if
a user accidentally deletes important data, that data is not
permanently lost.
Note: If a user removes a file in Drive or deletes a message from
the Gmail Inbox, the item moves to the Trash, where the user can
easily recover the item. When the user or the system empties the
Trash, this actually deletes the item. You can then restore the
deleted item.
References
1. Change your sharing settings - Drive Help
2. Transfer file ownership - Drive Help
3. Restore a user's Google Drive or Gmail data - Google Apps Help