Something done sine die has no definite date or period to resume. It’s legalese for “indefinitely,” and Latin for “without day.” If a meeting ends with no set day to get back together, it’s adjourned sine die.
When lawyers talk about a case being adjourned sine die, they mean that it was brought to an end without setting a date for another hearing or meeting. In other words, it's been paused for an indefinite period of time. In government, legislatures sometimes adjourn sine die, or without planning the next date to assemble. Sine die sounds like “sine-a di-ee,” not “sign die,” and is most often found near the courthouse.