(CNN) The government shutdown over President Donald Trump's proposed border wall has paralyzed the nation's already bogged-down immigration courts.

Judge Ashley Tabaddor, the president of the National Association of Immigration Judges, described judges in Los Angeles coming back this week to boxes filled to the rim with mail that had piled up over the course of the 35-day shutdown.

"Everybody did the best they could," Tabaddor said. "It's just a lot of trying to work with our hands tied behind our back."

The government shutdown centered on Trump's immigration agenda. His $5.7 billion request for his signature wall along the US-Mexico border, and congressional Democrats' refusal to give him that money, brought the government to a grinding halt -- including immigration courts.

Trump has repeatedly criticized the nation's immigration system, specifically taking issue with the practice of releasing immigrants while they await their court date. To remedy that, his administration has sought to hire more immigration judges in the hopes of unclogging the court. Even so, the shutdown seems to have put those efforts behind.

Read More