how to retrieve archived files
You have to set up Time Machine to have backups. There is no archive process since that is different than backup.

https://support.apple.com/en-us/HT201250

Short of you using time machine to look at that folder in the past, you would need to locate another copy of the file using spotlight in case you moved it to a different location.
Since you don’t mention your version, here is an article describing some clean up options.

https://support.apple.com/en-us/HT206996

The system doesn’t purge any files unless you set that up, and then only in trash.