The definition of “shelter” is telling: “A place giving temporary protection from bad weather or danger.”

Too often, those seeking protection from the elements at NYC’s homeless shelters aren’t protected from danger.

Last month, two stabbings at two homeless shelters occurred within days of each other. In the first, in East Harlem, a 62-year-old teacher was killed, allegedly by his mentally ill roommate. The incidents came about six months after Mayor Bill de Blasio unveiled NYC Safe, a $22 million effort focused on mentally ill individuals with violent tendencies. Goals included identifying those at risk, connecting them with treatment and support, expanding communication between key agencies, and adding officers and staff to high-need shelters.

So far, the partnerships haven’t fully materialized, and too many potentially violent and mentally ill individuals aren’t on the city’s radar. City officials note that the program is still new and problems are complex. To date, they say, NYC Safe is tracking 75 individuals, referrals are coming from the Department of Homeless Services, and mobile teams will start assisting mental health shelters this month.

But on this issue, we can’t wait for city bureaucracy to work at its usual snail’s pace. Adding security after an incident isn’t enough. A full ramp-up of NYC Safe must happen far more quickly. The city must better coordinate with mental health professionals and law enforcement, including police and prosecutors. The most vulnerable shelters must receive more resources and staff with expertise. And there must be oversight, creative problem-solving, more data collection, and measures of success and failure, so no one else slips through the cracks.

Most important, everyone must pay more attention. Those staying at the East Harlem shelter said they knew the resident who allegedly committed last month’s crime was becoming increasingly angry, that his violent threats were intensifying. No one listened. Nothing was done.

The city must employ staff, data-sharing, and know-how to make shelters safer. The shelters must be true shelters, and NYC Safe must live up to its name.