It depends on the type of debt you are referring to: is it based upon a written contract or an oral agreement? If it is based upon a written contract, the statute of limitations in Kansas is generally 5 years. If it is an oral agreement, then they have 3 years to sue on the debt. There are some other exceptions, but these are the general limitations.
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The debt balance will continue to accrue interest at either the statutory rate or the contractual rate. You can negotiate with the firm in a variety of ways, but they are not required to settle the case. Some ideas are to increase your monthly payment offer if they will "turn off" the interest, so that you will actually be able to pay the debt down. Another would be to make the monthly payments, then make lump sum offers (like the $1500), and if they won't accept those as payments in full, try...
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If you were late, look to the terms of the agreement at issue. If you don't pay pursuant to an agreement, you may be sued for breach of contract, which could result in a demand that you pay their attorneys' fees, more in interest and late fees, as well as court costs. I'd recommend not ignoring the demands to pay regardless.