in situations where there is no will, no named executor, the probate court would assign one - it could be a public guardian
as long as you are not the executor or estate administrator, you have no responsibilities for filing their past returns or any other returns that might be required.
here's what the iRS says
Tax Responsibilities of an Estate Administrator
A decedent and their estate are separate taxable entities. So if filing requirements are satisfied, an estate administrator may have to file different types of tax returns.
First, an estate administrator may need to file income tax returns for the decedent (Form 1040 series). The decedent’s Form 1040 for the year of death, and for any preceding years for which a return was not filed, are required if the decedent’s income for those years was above the filing requirement. For help, see the Filing the Final Tax Return(s) of a Deceased Taxpayer page.
Second, an estate administrator may need to file income tax returns for the estate (Form 1041). To file this return you will need to get a tax identification number for the estate (called an employer identification number or EIN). An estate is required to file an income tax return if assets of the estate generate more than $600 in annual income. For example, if the decedent had interest, dividend or rental income when alive, then after death that income becomes income of the estate and may trigger the requirement to file an estate income tax return. For help filing an income tax return for the estate see Filing the Estate Income Tax Return (Form 1041) page.
If the estate operates a business after the owner’s death, the estate administrator is required to secure a new employer identification number for the business, report wages or income under the new EIN and pay any taxes that are due. Publication 1635, Understanding Your EIN (PDF) provides information about this requirement.
Some or all of the information you need to file income tax returns for the decedent and their estate may be in the decedent’s personal records. The IRS can help by providing copies of income documents (Forms W-2 or 1099 for example) and copies of filed tax returns or transcripts of tax accounts. If you need these items see the Getting Information from the IRS page.
Third, an estate administrator may need to file an estate tax return (Form 706). Estate tax is a tax on the transfer of assets from the decedent to their heirs and beneficiaries. In general, estate tax only applies to large estates. For help with determining whether an estate tax return is required and how to file it, see the Estate and Gift Taxes page.
Additional information on the duties of an estate administrator is available in IRS Publication 559, Survivors, Executors and Administrators.
