It is very common to have a deceased person receive income after death. It is called Income in Respect of a Decedent (IRD).
Income reported in the name and Social Security number of a deceased person can be reported on their final tax return, even if it was received after death.
You are correct that can sometimes cause timing issues. If a taxpayer dies on December 29, 2020, the 2020 tax return will be the final 1040 for that taxpayer. Income received in 2021 would be reported on the estate return, or directly by the beneficiaries.
So to summarize, all 2021 income reported in the name of your relative can be reported on their 2021 final tax return.
If additional tax forms or income are received in 2022, you should report and /or deposit them in the estate.
If there is no estate, or if the estate has been closed, the beneficiaries should report the income as if it is their own income.
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