There is no time limit that I am aware of. The property would remain on the market until sold or until the beneficiaries give up and agree on a buy-out.
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I agree with Mr, Frederick.
As a general rule. there is no time limit on how long the home may be on the market. I have seen settlement agreements where the parties agree to a reduction by a set percentage (e.g. 5%) every six months until sold. But, again, that was by agreement of the parties in a settlement.
Laws vary from state to state and you should always consult with a local attorney regarding the law in your state.
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While there is no set time limit, the court could certainly impose a limit. Sometimes, to facilitate a settlement such as your buyout offer, it helps to lay all the numbers out for the plaintiffs and their attorney. If the house is sold to a third party, there will be all of the expenses involved with a sale that will come out of the proceeds first. You do not say if there is a mortgage on the property - obviously that has to be paid in such a sale. Broker's commissions, title insurance, and also, the new tax related to the health care law passed (Affordable Care Act) will all take a bite out of the proceeds. Compare those numbers to what the plaintiffs would get from a mutually agreed-upon buyout. Talk to a broker, and have them walk you through the potential expenses of sale if the property sells for a particular price. Use 2X the SEV for the example, although that may be on the high side for many properties. Once all the numbers are there to consider, they may do all the talking for you. Good luck!