The collection company is the party that typically will negotiate on behalf of the creditor; but it is important to contact the creditor to ensure that the collection company is acting at their direction (some collection companies aren't scrupulous and will fraudulently collect on unauthorized accounts).
Generally a collection company will settle for 50-70% of the bill if the party can pay a lump sum settlement. If a payment plan is required, they will generally only reduce the overall bill by 20%, but will often waive/freeze interest charges.
The fact that one moved does not preclude collections or a legal judgment, as the collection company typically has on retainer investigators who will assist in locating the consumer.
Also, if a person purposefully avoids service of process of a summons, the court can order that person to reimburse the creditor for the additional cost.
If one wishes to settle, they should draft a proposal, and send it certiifed mail, return receipt requested; or via fax. Then no agreed settlement should be paid until the terms are agreed to in writing.
It should also be noted that any waived principal will be chargeable as taxable income to the consumer, because the creditor typically files a 1099c with the irs, so they can write off the discharged amount.