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If the home was sold, by probate, the estate may have to pay capital gains tax. This is not considered the sale of a home by a business.
The FMV of the home is as of the date of death. If the home sold for less than that, then there is a capital loss, rather than a capital gain and no capital gains tax is due.
If a home is sold as part of a business activity, there is a sales tax that has to be paid. I mentioned this, because many people think that because they get an EIN number for the estate, that the estate is a business, and this is not the case.
You question was not very specific to exactly what you were asking, so I wanted to cover every potential.
In order for a person to get the capital gains exclusion, they had to have lived in the home and owned it as their primary residence for 2 of the past five years. This is to get the maximum capital gains exclusion.
There is a reduced capital gains exclusion if a person had lived in and owned the home less than the 2 and five, but that is based on the 5 years. If a home had to be sold because of unforseen circumstances such as:
Then a reduced capital gains exclusion would be available. But in your case it does not apply because the person stopped using it as a primary residence more than 5 years ago.
Living in a nursing home does not preserve the home as a primary residence.
You said you sold the home for less than market value.
The Fair Market Value of the home is the value of the home as of the date of death.
If you sold the home for less than that, there is no capital gains tax. It is a capital loss.