"If not, is a partial exclusion for deceased spouse available if surviving spouse's health has rapidly declined and can no longer live alone?"

It depends on when the surviving spouse moved out, and where that person moved to, for whether they still are eligible for their own exclusion. Is that what you are trying to ask with this question? Otherwise, the answer would be No.

A property isn't sold until the sale is Closed. Signed sales agreements fall through too often.

Is the taxpayer in a community property state? How was the property titled (name(s) on the deed)? Is it in a trust (what type)?