Good afternoon Rick,
I'm Doug, and I'm very sorry to hear of your situation. My goal is to provide you with excellent service today.
After a search of CT statutes, I find no law granting the buyer any type of unilateral extension for the closing of the sale, and therefore if you are not willing to grant them an extension of time to get their finances in order, then they are out of luck. Presuming that that there is nothing in the sale contract which would allow them to unilaterally force an extension of time, then you are no obligated to sign any kind of a written extension, not to agree to go forward with the sale of your property.
While many sellers agree to an extension based on a per diem payment by the buyer for the cost to the seller of the late closing. However, you are not obligated to try and negotiate this kind of a remedy.
You cannot prevent them from suing you, however, based on the facts that you have provided, I see no legitimate claim that they might have against you if you refuse to sign an extension at this late date and the closing never occurs.
You may reply back to me using the Reply link and I will be happy to continue to assist you until I am able to address your concerns, to your satisfaction.
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I wish you and yours the best in 2016,