The IRS only has 10 years to collect any tax debt you may owe. The clock starts ticking once the first tax notice goes out, regardless of whether you receive or respond to it. Once a decade has passed, the outstanding debt may possibly be forgiven if all attempts to collect have failed.
Before you get too excited however, remember that the IRS has many ways and means to recoup what's owed. Wage garnishments, liens and levies, and asset seizures are some of the powerful tools at their disposal. The IRS use these collection tools sooner than the 10-year mark if you ignore notices or do not attempt tax resolution.
Under certain circumstances, the IRS is also to extend the statute and pursue collection for longer than a decade. Don't try to beat the clock. Seeking tax resolution is always your best option.