Is sounds as if you may have two separate issues here? A financial hold on your records due to unpaid tuition, etc. should have nothing to do with deletion of academic records. In fact, most universities do not allow one to continue with class(es) for the semester if tuition goes unpaid (unless agreed upon in advance) -- you're forced to "drop" the class, with no academic penalty. In the event you withdrew from school, whether officially or not, if you were enrolled in class past a certain date, and didn't finish (i.e. take finals, etc.) -- those grades could potentially convert to "F's" if not resolved within a specified time frame, AND then become part of your permanent academic record.
I don't know that you can negotiate removal of academic evidence of enrollment through agreement to pay your tuition and/or remaining fees. Certainly, traditional universities and colleges do not practice that.
If you could provide a bit more information, maybe someone could offer the best course of action? Best of luck!
Starting Score January 1, 2010: 640
Hi Shooting Star,
I appreciate your response. During this time I was very unstable and without a doubt I did not handle the situation correctly. I did not drop the courses, so it is very likely that the final grade you mentioned could be represented on my academic record. I haven't personally seen it, but I also consider it a remote possibility that the instructor's of the courses might have removed me, due to my lack of attendance.
I guess what I'm curious about is bargaining. I fear it because there is no assurance that if, once they receive such a letter they might attempt litigation for failure to pay this tuition. I just don't know what would be the best course of action, especially whenever the university isn't very UNwilling to communicate.
It's very clear that this proposal has no historic evidence to provide understanding of whether it's possible or not.. I've found nothing like it on myFICO.
I have no problem paying the un-paid tuition.. but kind of like you said, I don't know what the best course of action is. Just seeking input, advice or the idea of a possible solution. Thank you for your reply! 
Depending on the type of institution you attended, there may be a process by which they could retroactively grant an "official withdrawal" which would certainly be much more kind to your academic records. If I were you, I would talk with a Dean of Students, Registrar, and/or Advisor to ask where to begin. Many universities have policy pertaining to unique and extreme circumstances of retroactive withdrawal (and also reinstatement), etc. (eg. relating to mental or physical health issues, family issues, etc.). Understand that whatever your particular circumstances were will need to be substantiated by appropriate documentation, etc., but I would definiately approach this issue from two separate angles -- academically and financially. Especially if you're wanting to continue with school...
[Edited for clarification: When I suggest approaching from two angles, I meant not to combine the two issues, necessarily. They may treat your unique academic situation more kindly if you not attempt to nogotiate removal of any negatives with an agreement to pay. But again, it depends on the TYPE of institution (non-profit/traditional vs. for-profit).]
Try not to get discouraged -- I would still attempt to straighten out the academic side of things ASAP. There has to be a formal appeal process by which you can discuss the extreme circumstances of your situation -- and go from there. You'll never know -- they may be willing to help you straighten things out. Academic advisors have nothing to do with your tuition -- they should be able to help you discuss your ACADEMIC reality and options available to you REGARDLESS of your financial situation with them. I would start there. Hopefully you're able to get this resolved!