A tax return should have been filled for the years that his income was over $25,000. By failing to file it is possible that the IRS will take his information and create a tax return for him. If there is a deficiency based on the created returns then they will send the notices to him for the tax years. Only your father is liable for the failure to file so you do not have any responsibility here. Given that he is sick, has no assets and in a nursing home there is really nothing that the IRS can go after if he did under pay. Further, given that your father's income is all going to the nursing home he will have an extensive medical expense deduction which means he will likely owe no tax.
With all that said, you are safe to just wait to see if the IRS generates a return with a deficiency in tax. However, you may want to see if he is having income tax withheld from his pension already. If he is then you may find that he is owed a refund for overpayment of tax due to the large Medical expense deduction for the nursing home payments.
I cannot provide you with legal advise. I have provided you with information about the law related to your question. My answer, and any information that you find online, should not take the place of having a consultation with a lawyer in your area to advise you regarding your specific issues.
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