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Many states do have a statute of limitations on collecting property taxes. For example in Texas:

Sec. 33.05. Limitation on Collection of Taxes.

(a) Personal property may not be seized and a suit may not be filed:

(1) to collect a tax on personal property that has been delinquent more than four years; or

(2) to collect a tax on real property that has been delinquent more than 20 years.

You would need to be more specific about the state you are interest in before you click ACCEPT if you require specific information.

re they being asked to pay the taxes

sorry* Are they

Let me see if Illinois even has a statute of limitations on proeprty tax

property*sorry

Thanks for waiting, I had to wade through the codes

(35 ILCS 200/20-190)

Sec. 20-190. Statute of limitation for collection of delinquent real estate taxes and special assessments.

(a) If a Taxpayer owes arrearages of taxes for a reason other than administrative error, actions for the collection of any delinquent general tax, or the enforcement or foreclosure of the tax lien shall be commenced within 20 years after the tax became delinquent, and not thereafter. After 20 years the tax lien shall be discharged and released.

They do have a statute of limitations but you can see it is 20 years

I am at a loss to understand how any property taxes not paid were overlooked at the time of sale

You are welcome

If this were the IRS that you were dealing with I would advise you to request to be placed on Currently Not Collectible status. This means that your income is not sufficient to support a tax debt be satisfied. This appears to be dealing with a private company and out of the tax area now

I would suggest you request the aid of an attorney if this is a legal matter with a private company

Best wishes