Someone should file a final tax return, that is the duty of the personal representative (might be the executor of his will or his next of kin). The final tax return only reports income, deductions and credit that happened up to the day he died. Income paid after he died is handled differently, I will discuss that later.
If he owes taxes, the money comes from his estate (property, bank accounts, etc.) The heirs are generally not entitled to anything from his estate until his legal debts are paid. This is governed by state law, but if you kept his car or his bank account or you inherited and sold his home, you are not legally entitled to keep that money until you settle his debts including taxes. So if he had no money, you are not required to pay for him, but if he had money, you have to pay those taxes out of what he left you before you can keep the rest. (If there were several heirs, and you already paid out the funds, then each heir owes an equal share of the taxes back to you so you can pay them.)
You may need to go to probate court in your state and file some forms to prove you are the person entitled to handle his affairs including his tax return.
Here are some articles.
https://turbotax.intuit.com/tax-tips/family/death-in-the-family/L5albFXM4
https://blog.turbotax.intuit.com/tax-planning-2/real-talk-series-my-mom-died-this-year-how-do-i-file...
https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-forms/forms-need-filing-tax-return-s...
If income was received after he died, there are two options I can talk about. Income received after he died is considered to be paid to his estate. His estate is a separate legal entity from himself, and comes into existence when he dies. And the estate needs to file its own separate tax return.
However, if the income is relatively minor, and you are the person who is entitled to it by law (as next of kin for example) then you can report that income on your tax return as "income in respect of a decedent."
