The city has scrambled for years to create more housing of the sort that would entice homeless people off the street. Mr. Adams’s predecessor, Bill de Blasio, opened several thousand beds in so-called low-threshold shelters that offer private rooms and fewer rules and curfews than traditional shelters. But those rooms remain in short supply. Meanwhile, the city has stepped up its destruction of homeless encampments.In the wake of the 2019 killings of four homeless men who were sleeping on the street in Chinatown, the city said it would build more shelters in the area. Recently, it announced plans to open three private-room shelters in Chinatown.But, in part because of an increase in anti-Asian attacks, the proposed shelters have been loudly opposed. Shelter opponents quickly raised over $100,000 for a planned lawsuit. Last month’s Lunar New Year parade included demonstrators urging Mr. Adams to “save Chinatown” by canceling the shelters.One of the proposed sites, scheduled to open later this year on Grand Street, is just seven blocks from where the man sleeping in the doorway was killed on Saturday.In Washington, the homeless population has been declining for years, as more resources have been made available to homeless families and veterans. But as the city becomes ever less affordable, the number of chronically homeless single adults has not declined, and, according to the 2021 survey of the homeless, it rose during the pandemic.Given the fears of the Covid-19 era, several advocates for the homeless said, more people had been living outside rather than in communal shelters. Some came together for safety in small clusters in parking lots or construction sites, while others set up tents on sidewalks outside of the sleek office buildings of downtown Washington.The recent shootings show how crucial it is to address homelessness through programs like housing vouchers and other investments, said Christy Respress, the executive director of Pathways to Housing DC, a nonprofit group.