Yes, use a Mirror, which will replicate deletions too (Backups specifically delete nothing). If you're concerned about accidental source-deletions being replicated to the destination, you can use Versioning set to keep [1] copy for [as long as you want]. Anything deleted or replaced* on the Destination by the profile will be stamped 'when that happened' and moved to a hidden repository. Such Versions won't by default be Restored in a bare-metal Restore (but you can cherry-pick them to recover from accidents).
* Note that Versioning will also store the previous-recent copy of any files that change, too. You may find that a blessing or a curse, but it's not debatable. Versioning is designed to capture changes - we just treat deletion as a fairly drastic change...
* Note that Versioning will also store the previous-recent copy of any files that change, too. You may find that a blessing or a curse, but it's not debatable. Versioning is designed to capture changes - we just treat deletion as a fairly drastic change...