The capital loss carryover is not $3,000 per year. The capital loss carryover is the total amount of losses that have not already been used. All of the capital loss carryover, up to the total amount, can be used to offset capital gains. If the entire capital loss carryover is not used to offset capital gains, up to $3,000 of the remaining unused loss can be used each year to offset ordinary income.
There is no special rule for the year of your death. Any capital loss carryover that remains unused on your final tax return is gone.
