You may want to consider filing a motion to enforce the settlement. However, this would be very difficult in that it appears to only be an oral contract and there does not appear to be any support to your assertion that funds were paid to satisfy the debt in full. The process to enforce the settlement would be difficult to accomplish on your own and may take an excessive amount of time and effort. Of greater concern is the damage that this has already had upon your credit rating. I would highly encourage you to seek the advise of a qualified bankruptcy attorney to address your financial issues. A bankruptcy could be utliized to restore your credit and give you a "fresh start". In the interim, my concern would be that the collection agency will continue efforts to collect on the the prior lease deficiency while simultaneously creating more damage to your credit.
The first question is were you actually sued civilly. This is different from being taken to landlord tenant court to be evicted and allow the landlord to retake possession. If not, then the debt collection agency is simply trying to collect on the outstanding unpaid rent. Your first step should see if you are dealing with a collection agency or an actual attorney hired to sue you for that unpaid amount.
Usually collection agencies have a minimum amount of a "Settlement" they are allowed to accept (based on what your old landlord will accept). However, if you pay this bill less than the full amount owed; the reporting on your credit report most likely will reflect "account settled for less than the full balance". Previous attorneys have mentioned a bankruptcy and I second that recommendation. If you are having financial troubles that extend beyond this one obligation; perhaps you should sit down with an attorney to go over your entire financial picture. Good luck!
Please note this is to be considered general information and not legal advice about any particular situation. The answering of any question does not create an attorney client relationship and does not make the answer given here specific legal advice. If you wish to obtain legal advice; then please do consult an attorney with your issue. I am an attorney licensed in New Jersey and Pennsylvania. In handling bankruptcy, and helping individuals seek relief under the bankruptcy code, my practice has proudly been deemed a debt relief agency.