As a general rule, there is a ten year statute of limitations on IRS collections. This means that the IRS can attempt to collect one's unpaid taxes for up to ten years from the date they were assessed. Subject to some important exceptions, once the ten years are up, the IRS has to stop its collection efforts.
The ten-year limitations period is not absolute. It can be extended if one voluntarily agrees to do so. Back in the bad old dates (before 1998), the IRS used to put enormous pressure on taxpayers to agree to extend the limitations period beyond ten years--such extensions often lasted for ten or even twenty years. If the taxpayer refused to "voluntarily" agree to the extension, the IRS would make threats. Fortunately, this is no longer allowed.
However, if one enters into an installment agreement with the IRS allowing for partial payment of the amount due, the IRS will likely have one sign a form waiving the ten-year limitations period; however, this extension can be no more than six years. If one's limitations period is nearing its end and still owes the IRS substantial money, IRS personnel may offer an installment agreement with attractive terms in order to get one to agree to extend the collection deadline. Consider carefully before agreeing to any such extension. One may be better off refusing to extend the deadline and let the IRS collect whatever it can before it runs out.