LOS ANGELES — The federal government shutdown last year delayed more than 37,000 immigration hearings by months or years for immigrants already waiting in lengthy lines to plead for asylum or green cards.

While the country’s immigration courts are now running as usual, immigrants who had hoped to have their cases resolved in October so they could travel abroad to see family or get a job have instead had their lives put on hold. Many had already waited years to get a hearing date in the notoriously backlogged courts, which determine whether immigrants should be deported or allowed to stay in the country.