You are confusing an accounting entry with a legal obligation. The obligation to pay the bill never goes away. The original company makes an accounting journal entry that says "we no longer believe we can collect this debt from this deadbeat, so we are taking the loss on our books now" (this does not relieve the debtor for his obligation - in fact it has nothing to do with the debtor). The original lender then sells the debt to the collection agency for say 10 cents on the dollar (in your case, they probably recouped $20). The collection agency now owns the debt with all the legal ramification associated with that debt. That includes the statute of limitations which means, basically that after a certain amount of time (say 3 or 4 years), thee gancy can no longer use the court system to collect - that, however does not mean the debt goes away, you still owe it. Then, assuming the debt got sold to a normal collection agency, the next time fame isi 7 years after default - which is when the collection account will fall off your credit report (again, the debt does not go away, it just can't be reported).
You have three options - 1) pay the $200 and get the account marked closed/paid in full; 2) settle with the agency for an amount less than the $200 in exchange for the account account being closed (it will be marked payed/settled). 3) Ignore it until the 7 years runs out (which means you will have trouble opening new accounts for the next 7 years until the account drops off your credit report.