Since you estimate that taxes will be owing for your parent's final year tax return, you should file a return. If taxes are owing, getting an extension will not relieve your parent's estate of liability for late payment penalties. It would be possible to file an extension form along with an Estimated Tax Payment which, if sufficient in amount, would avoid such penalties. If your parent's estate has no assets, as you indicate, there will be no way for the IRS to collect the amount of taxes owing. You would only be liable for payment to the extent of any assets you inherited.
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To file taxes for a deceased person, you generally need to file and prepare the final individual income tax return the same way you would if the person were alive1. Report all income up to the date of death and claim all eligible credits and deductions. If the deceased had not filed individual income tax returns for the years prior to the year of their death, you may have to file1. If there is not a surviving spouse, someone needs to be chosen to file the tax return, such as the estate's executor or administrator2. To prepare the return, you will need to access financial records and may need to provide a certified death certificate2. If there's no appointed representative and no surviving spouse, the person in charge of the deceased person's property must file and sign the return as "personal representative"3. If filing a paper return, write the word "deceased" along with the decedent's name and date of death at the top of the 1040 or 1040-SR4.
