I disagree. Most states do have various limitations on both assessment and collection of at least some of their taxes, most notably income taxes. But what is very common is that there is no statute of limitation for assessment of taxes for which returns are required if the taxpayer never filed the return.
Berdaaz, it would be important to know when the tax was assessed. It is also significant to know how the business was organized — was it a LLC, corporation, or what? If you did have a separate entity like LLC for the business is this assessment against just the business or against you personally? And what about the bankruptcy, did you file bankruptcy personally, did the business file bankruptcy, or both?
Even if the assessment is legitimate, the answers to the above questions will determine whether the state can actually collect it now. For example, if the business was a LLC or corporation and the tax is assessed against that LLC or corporation then the state is going to be out of luck because I presume that business has been defunct for many years and has no assets for the state to grab.
For the future, one record you always want to keep for ever is copies of your returns, proof of payment, and any proof of filing you have for them, since the general rule often is that the statute of limitation for assessment of tax does not start to run until the returns are filed you want to show that you did file the returns in question if the states come back many years later and claims they weren't filed. Except in unusual situations the IRS does not usually go back more than 6 years to chase returns that have not been filed, but many states have gotten a lot more aggressive in the last 15 years in dredging up old data and pursuing what they believe to be unfiled returns that were due.