As Beacon Hill tries to envision a future for the state’s beleaguered shelter system, a key lawmaker is looking optimistically at how quickly new arrivals are getting authorization to work in the United States.

The emergency shelter network in Massachusetts has strained to accommodate unprecedented levels of demand over the past year, driven by families moving here from other countries and a housing affordability crisis that challenges newcomers and longtime residents alike.

An April state law that poured millions of additional dollars into the shelter system also created a special commission to study the “sustainability, efficiency, and effectiveness” of the emergency housing program and make improvement recommendations to lawmakers.

At a commission meeting Monday, officials from Gov. Maura Healey’s administration said about 3,900 migrants living in shelter are now authorized to work in the United States. Counting migrants who have since moved on to other housing, that number stands at 4,515.

While Healey’s team put forth some restrictions on shelter access to ease ballooning costs, the administration has also pushed to connect migrants and other new arrivals with work permits and resources to find and train for jobs here so they can ultimately land in more stable housing situations. Last fall, Massachusetts partnered with the federal government to host streamlined work authorization clinics.

As of August, a total of 4,884 shelter residents and people who have recently exited shelter reported being employed or enrolled in training programs, state data shows. That number includes U.S. citizens and permanent residents as well as the holders of work permits.

State Rep. Jim Arciero, a commission member who also co-chairs the Legislature’s Housing Committee, said the figures give him “a sense of optimism,” as one of the main questions confronting policymakers is “about people getting jobs and moving forward.”

“First, I’d like to say this is an enormous challenge, right, and I don’t think we talk about it enough, and probably for a lot of us, it’s going to be one of the most enormous in our public service career,” said Arciero, a Westford Democrat. “But what gives me a lot of optimism we’re moving in the right direction is the work authorizations.”

The at-capacity shelter program houses around 7,500 families. Lt. Gov. Kim Driscoll, who chairs the commission, said one of the panel’s goals is to plot out a sustainable shelter system while also meeting the varied needs of different types of families – for instance, new immigrants, a Massachusetts family evicted after a job loss, or a single mother escaping domestic violence.

State Sen. Robyn Kennedy, a Worcester Democrat, said she wants to see the state “willing to think really differently” and become more proactive about how it approaches shelter and related services

“What we haven’t been able to do is create a system that is family-centered, that actually meets a family wherever they are in the state and helps them with whatever needs that they have in the moment, ideally even maybe ten steps before,” she said. “The family that walks into MassHire because they lost their job, that’s an indicator housing instability is maybe only a matter of months away.”

The shelter commission faces a Dec. 1 deadline to file its report.