IRS has ten years from the date of assessment to collect the unpaid tax liability, unless some action of the taxpayer extends it beyond the 10 years. Common examples are filing of bankruptcy, leaving the country to reside elsewhere, signing a voluntary waiver in relation to an offer in compromise or a payment agreement, etc. IRS may also extend it indefinitely by suing in the U.S. District Court and reducing the liability to a judgment. (The judgment for the tax liability against Al Capone is still outstanding and could be collected at any time – if IRS can find him or any of his assets.)
With some rare exceptions, once the collection statute expires the IRS can no longer pursue collection of the tax liability. It must then abate the tax and release any liens filed against the taxpayer's property.