There is never a tax deduction for ordinary living expenses, either for you or your dependent. The only tax break for an adult dependent is the $500 credit, and you can only claim them as a dependent if they are alive during the year. Your adult parent can be your dependent for 2021 if they meet the other qualifications, even though they died partway during the year, but they cannot be your dependent for 2022.
There is a special exception for medical expenses. If you paid medical expenses for the person in 2022, you can deduct those expenses as itemized deductions on your 2022 tax return, as long as the person was your dependent when they passed away, even though they cannot be claimed as your tax dependent for 2022.
The IRS says in publication 502,
What if you pay medical expenses of a deceased spouse or dependent?
If you paid medical expenses for your deceased spouse or dependent, include them as medical expenses on your Schedule A (Form 1040) in the year paid, whether they are paid before or after the decedent's death. The expenses can be included if the person was your spouse or dependent either at the time the medical services were provided or at the time you paid the expenses.
