The worst they can say is no. This is a collection agency, not the original creditor. They probably bought the account for pennies on the dollar. Tell them you are broke and if they want to get paid anything, this is what you can afford to pay. Don't give them any other information, just the offer. Get a letter from the collection agency stating they will accept the $200 and take the collection account off your record before you send them any money. If they don't accept $200 with an agreement to take the black mark off your credit, you can always try again in a month. The goal is as much to get them to take the collection off your record as it is to pay a reasonable amount for the service received.
Until this is resolved, you will have a tough time getting credit. Get it behind you so you can move forward with your life.