Huge Library Cache file, and other file problems

On June 1, I had an issue with a corrupted library (I can't remember the exact message I got), and FCPX created a repaired library for me. That new library seems to function perfectly, I have been using it intensively for the last week. All the old events and projects seem to be it.

Logic tells me that I can delete the old problematic library, and the associated Library Cache package. But I would HATE to do something that I regret, so I thought I would ask here first. Is it safe to trash the first and last items in this folder (pictured below)? Obviously I am especially interested in that almost-4T Library Cache file. How did it get so big? If I have deleted the transcoded files (render, proxy and optimized) files for inactive projects, shouldn't that Cache file be pretty small? Even with the repaired and current Library, the cache file is 293GB. I have searched the internet trying to learn more about that file, I don't see a good explanation, or something that tells me how to slim it down (other than deleting those render etc. files).

Any help would be greatly appreciated. Thanks in advance, Peter