What precisely do you mean by "Library entry"? The first term "Library" is used in Lightroom but not in conjunction with "entry". So "can I remove the Library entries that are in my Library's List of each property I've shot from my library?" could mean anything. And what does this mean - "What I'd like is to put all my Finished Jobs into collections, leaving only the Open jobs in my Library, less possible confusion"?
I'm not being awkward, but one could answer your question more helpfully if you would go over it again and use LR terms much more tightly. Maybe add some screenshots to show the problem?