If you set it to use Versioning on Destination and keep [1] copy for [7] days, it will - on the full/rescan - Version the original (now-deleted) file, and keep it for a week. Note that it will do so for any changed files, too. There's no distinction in Versioning between changes and deletions (we just treat deletion as a fairly drastic change...), and that won't be altering. But those changed-file Versions it also makes will also age/expire (and get replaced with newer ones, though not necessarily of the same files) once a week on a rolling basis, which limits the extra space required. If you want to actually keep them for longer than that extra week, adjust the expiry limit to suit, though you'd potentially need to have (more) available space.
Note that the Versioning will have no effect on the Incremental backups, because those locations are (presumably) mass-flushed before the scan (to remove out-of-date changed files), and are thus empty by then. You cannot make Versions of files that are not there...
Bear in mind there is no rule that says you can only make one backup, by the way. Generally we recommend you have at least two, on different devices and maybe even different locations.
Getting back to your previous issue, it doesn't make a lot of sense for there to be 'no files to copy' on a rescan if there are files present in the 'preceding' (earlier date) Incremental locations. If there are, it must have detected these were new or changed...and they presumably now represent differences between the previous full backup and the refresh thereof.
Incidentally, if you have lost the 'Monday' log already (by Friday), this suggest either you changed the standard logging options to keep 'last 5' logs (or the per-profile override) or you are running the profile more than once a day, which you absolutely should not do (as per the Help: "You should schedule the profile to run just once every day"). You may want to set the per-profile logging override to cover at least 7 days, possibly 14, if you want to detect patterns.
Note that the Versioning will have no effect on the Incremental backups, because those locations are (presumably) mass-flushed before the scan (to remove out-of-date changed files), and are thus empty by then. You cannot make Versions of files that are not there...
Bear in mind there is no rule that says you can only make one backup, by the way. Generally we recommend you have at least two, on different devices and maybe even different locations.
Getting back to your previous issue, it doesn't make a lot of sense for there to be 'no files to copy' on a rescan if there are files present in the 'preceding' (earlier date) Incremental locations. If there are, it must have detected these were new or changed...and they presumably now represent differences between the previous full backup and the refresh thereof.
Incidentally, if you have lost the 'Monday' log already (by Friday), this suggest either you changed the standard logging options to keep 'last 5' logs (or the per-profile override) or you are running the profile more than once a day, which you absolutely should not do (as per the Help: "You should schedule the profile to run just once every day"). You may want to set the per-profile logging override to cover at least 7 days, possibly 14, if you want to detect patterns.