Can a 10 year old state tax debt be included in a Chapter 7 matrix in a bankruptcy filing?
Generally, bankruptcy will not protect you from a tax debt and you would not be able to include this in your Chapter 7 bankruptcy.
The short answer is "possibly". It depends on how long the taxes have been past due, when the returns were filed, and why the taxes are owed (e.g. income, employment, excise, etc). Specifically, only income taxes may be discharged in bankruptcy. Other taxes, such as excise, estate and gift taxes are not dischargeable. As for payroll taxes, there are 2 portions which make up a payroll tax return - the trust fund which are the taxes withheld from the employees and the non-trust fund which are the taxes paid by the employer. Only the non-trust fund portion can be discharged and that is normally around 1/3 of the total tax.
Note: Trust fund penalties and fraud penalties are never dischargeable.
You should consult a DE bankruptcy lawyer to about the specific facts of your case.