There are a couple of issues.
1. If you live in a community property state, the surviving spouse receives a fully stepped up basis equal to the fair market value on the date of the spouse's death. This may need to be determined by appraisal. The basis is the spouse's new basis, and does not expire.
2. If the surviving spouse sells the house in 2 years or less, and has not remarried, they can claim an exclusion of the first $500,000 of capital gains. If more than 2 years has passed, they claim an exclusion of $250,000. (Possibly $500,000, if they have remarried and the new spouse has lived in the home more than 2 years and has not used their own exclusion in the past 2 years.)
3. However, the amount of capital gain that is subject to tax is only the increase in value since the stepped up basis as of the spouse's death.
For example,
You bought the home with your spouse in 2000 for $200,000. Your spouse died in 2021 and the FMV of the home at that time was $500,000. You sell in 2025 for $700,000. Your capital gain is $200,000. As long as you lived in the home as your main home for more than 2 out of the previous 5 years, you can exclude the first $250,000 of gain from your taxable income. Since the gain is less than the exclusion, the gain is not taxable.
