Generally, once the debt is turned over to a collection agency, you must deal with the collection agency. Try to explain your situation to the collection agency; they may be able to settle the debt for less than the total owed to the collection agency now.
The doctor or hospital, after an account becomes delinquent, may direct all management of payments to a debt collector. Some of my clients have been successful in going back to the original creditor (the doctor or hospital) to resolve the account. But by and large, the original creditor wants you to deal with the debt collector and has either written off your debt or given responsibility to a third party. I don't believe it will hurt you to try.
Like Jill stated a Debt Collector is often willing to settle for less than the amount owed. Debts that are written off are generally sold to debt buyers for pennies on the dollar so if you owed $100 the debt buyer may only pay $10 for it, or less. Of course there are some other technical issues that make it a profitable situation for the creditors and debt buyers/collectors.
You should definitely try negotiating with the debt collector first. They have the incentive to get you to pay and will be willing to negotiate. Be warned they are experienced and will they and get you to tell them how much you can pay. Try and get them to give you a number first so that you are negotiating them down instead of you being locked in at a higher price. If the debt collector has been abusive, harassing, or threatening in any way you may want to forgo payment until you have spoken with an attorney in your state who practices under the Fair Debt Collection Practices Act(FDCPA), a federal statute that protects against collection abuse. Use Avvo or naca.net to locate an attorney in this practice area.