If they are not responding its likely that it is because they are not accepting the offer. You should try and contact them by phone and see if you can speak with someone, perhaps the attorney you sent the letter to. However, keep in mind that if they are already garnishing your wages, the incentive to settle for a lump sum at 50% when they are already receiving money from you is low.
First you should call the lawyer to see if he has contacted his client regarding your offer. Sometimes lawyers get busy and they need a little push. The lawyer will then let you know whether the offer has been accepted, countered or simply rejected. Don't tell him you want to hurry the process to buy a house. You don't want the lawyer to think you feel any sense of urgency in the matter. Unless the creditor needs a quick infusion of cash your offer will probably be rejected. Good luck.
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If they have a wage garnishment, they have very little incentive to settle. And even then, the settlements they are likely to accept (after a judgment and a successful garnishment) tend to be north of 50% of the balance owed. But again, with an active, successful garnishment, there isn't really much you can bring to the table.
Instead of sending letters, you should be calling. In the collection industry, settlement papers (the letter) is ALWAYS generated by the collector, not the debtor. So, you get on the phone, hash out the settlement (assuming you can get one) and then THEY send you a settlement offer letter. Collectors will almost never respond to a written settlement offer from the debtor and they will NEVER accept it. They letter has to come from them.
If they are already taking money out of your paycheck the likelihood is that they don't want to settle. You should call them and try to speak to the attorney maybe he/she may be willing to take a lump sum.