If there was some payment plan or other agreement as to payment--even an oral one--that agreement would be enforceble, and they could not sue you as long as you were honoring your obligations. However, without a plan or an agreement with the collections agency as to payment, they may sue you, even if you have been voluntartarily paying what you could.As for whether you should continue to pay or not--assuming you legitimately owe the money AND document/prove all payments you make, you may wish to continue paying, assuming you have the money. Anything you provably pay will reduce what you would owe in a lawsuit (so the money is not going to waste) and will also demonstrate good faith (that you are paying what you can).