The extra-territorial jurisdiction of a Court notwithstanding that a person does not reside within the territory, but upon that person, because of some event which by its nature, extends the Court's jurisdiction to beyond.
Each court is bound to a territorial jurisdiction and does not normally have jurisdiction over persons that reside outside of that jurisdiction. For example, a court in Scotland would not normally have jurisdiction over a resident of Ireland. Long-arm statutes are a tool which gives a court jurisdiction over a person even though the person does not or no longer resides in the territory limits of the court.
For example, UIFSA allows a court to have jurisdiction over a non-resident support payor.
Although jurisdictions differ on points of detail as to the extent of personal or commercial contact required before a person might be captured within a state's judicial jurisdiction under the tentacles of long-arm jurisdiction, a person who transacts business, owns property, enters a state's territory or commits a tort or a crime on the territory while passing through, expose themselves to long-arm jurisdiction.