I think there is a bit of nuance here to consider. The restaurant, bar and hospitalities industries have been hit pretty hard by the pandemic. The majority of people who lost their jobs due to covid qualified for unemployment benefits; undocumented aliens did not. For at least the first 6 months of the pandemic, unemployment was paying $600 a week in NY.
Undocumented workers are a big part of the support staff in restaurants bars and hospitality industries. This is a one time payment where many people have collected far more than that since march. While the stimulus checks were for everyone, regardless of current work situation, unemployment checks were not, leaving undocumented workers financially stranded with no way to support their families despite only being out of full-time work due to the pandemic. Undocumented workers didn't even qualify for any of the stimulus payments.
It would be a huge financial blow and disrupt the NYC economy if all undocumented workers became homeless at once.