Can a debt collector raise the settlement offer once they make a lower offer?

Not if you have a hard copy of the SIF (settlement in full) offer. If you have that and you are within the terms of the SIF (the payment due date has not elapsed) they will have difficulty raising the amount. I wonder why you would want to settle. Don't you realize how that is going to haunt you for years?

If they offer you a settlement, demand a settlement letter prior to agreeing to any terms. Have them fax it to you immediately.

Obviously answered by a non-lawyer. An offer to settle can be revoked or changed at any time before it is accepted. Even then, it may be necessary for there to be some written agreement, if it involves payments over more than a year (Statute of Frauds), or some payment or change in position based upon the offer or the acceptance of the offer (called consideration).