In answer to the question "Is there a way to automatically send deleted files to a specified folder? " - yes there is - or at least, a way to achieve this same thing - using autoarchive.
In the properties of the Deleted Item folder, go into Auto Archive, and set it to move to an Archive PST. Choose how many days old as a cut-off. Then, set Auto Archive to run frequently ( I have it set to run daily without prompting).
I do this at work because their Exchange policy deletes everything over 7 days old from Deleted Items, so I save them to the archive PST.
P.S. One other tip, to backup your Archive PST if it is large, try "Mailstore Home" - it creates backups that are incremental in effect - by splitting its backup output into files of about 10MB so that you don't have to re-copy the existing ones.