A post from Elon Musk last month trumpeted a supposedly startling discovery by his team of government cost-cutters: The Federal Emergency Management Agency had provided $59 million to house undocumented immigrants in New York City. The money, he declared, was “meant for American disaster relief and instead is being spent on high end hotels for illegals!” But if Mr. Musk’s goal was to funnel more FEMA money to disaster aid, the fallout from his declaration had the opposite effect. A pair of Trump administration orders, issued soon after the Feb. 10 social media post, aimed to block any agency money from helping undocumented immigrants and “sanctuary” jurisdictions protecting them left FEMA staff without sufficient guidance about how to proceed, effectively freezing payments on billions of dollars in disaster grants, according to two people briefed on the process and an internal document viewed by The New York Times. While the freeze did not stop aid going directly to disaster survivors, it has disrupted payments to states, local governments and nonprofits, with ramifications being felt across the country. In Florida, a nonprofit that helps hurricane survivors find housing and other services noticed its promised FEMA payments stopped coming, raising fears that it will have to trim operations. In southeastern Michigan, communities hit by devastating floods two years ago are waiting for federal money to cover the cost of rebuilding. And in Helene-ravaged western North Carolina, tiny Warren Wilson College, a liberal arts school that specializes in environmental and climate science, has been hoping to hear in recent weeks about an application for aid to repair damaged roofs and clear debris from research fields, but has heard nothing. “There’s a deep sadness when walking through all that debris, knowing all that was lost,” said Rosemary Thurber, a 22-year-old student at the college whose studies have been disrupted. She said that she and her fellow students were “losing faith in our federal government.” The funding freeze illustrates the extraordinary power of Mr. Musk, the world’s wealthiest man, who has increasingly pointed his Department of Government Efficiency at exposing funding that benefits undocumented immigrants and whose demands regularly prompt responses from senior government officials. In this case, Mr. Musk’s 5:03 a.m. post on X, the social media platform he owns, was followed hours later by a memo from Cameron Hamilton, the acting head of FEMA, saying the agency had stopped payments under a variety of grant programs, and given DOGE “full system access to our financial management system.” Nine days later, Homeland Security Secretary Kristi Noem, whose agency includes FEMA, signed the first of two agency orders that took aim at migrant funding and effectively spread the freeze across almost all of the agency’s grants. After The New York Times submitted a list of detailed questions about the freeze on Monday, Ms. Noem on Tuesday signed a memo authorizing agency staff to exempt certain grants from the immigration-related orders, according to a person briefed on the change. It is not clear when or how quickly FEMA will go about releasing the money, and the Department of Homeland Security did not respond to The Times’s questions. A representative for the White House and DOGE did not respond to questions this week. The FEMA press office said in a separate statement last week that it attributed to an unnamed homeland security official: “FEMA is taking swift action to ensure the alignment of its grant programs with President Trump and Secretary Noem’s direction that U.S. taxpayer dollars are being used wisely and for mission-critical efforts.” The freeze has played out against the backdrop of widespread upheaval at the disaster relief agency, highlighted by Ms. Noem’s assertion during a Monday cabinet meeting that “We’re going to eliminate FEMA.” Ms. Noem’s office has directed staff to develop a plan to disband the agency, according to a person familiar with internal deliberations who was not authorized to discuss the matter in public. It is not clear what government agencies, if any, would take over FEMA’s role delivering aid to communities hit by disasters. Mr. Trump has mused about returning those duties to the states, or perhaps having the Defense Department carry more responsibility for responding to disasters. In the short term, however, many communities that see FEMA grants as a lifeline are still waiting. “There are projects beyond our ability to address on our own,” Damián J. Fernández, the president of Warren Wilson College, said earlier this month on a campus still covered in debris from the September storm, his voice breaking. “We have followed the rules. But the system is not working.” One storm leads to another FEMA’s existential crisis arguably began last fall, when Hurricane Helene killed more than 100 people in North Carolina and damaged more than 73,000 homes. The destruction was shocking, especially in a region not accustomed to hurricanes, and quickly became part of the presidential campaign. Within a week of the hurricane reaching North Carolina, FEMA had provided more than $45 million in disaster relief and sent more than 1,500 personnel, according to the agency. But as survivors struggled to regain access to basic services, many concluded that FEMA was failing to do enough. That message was amplified by Mr. Trump and Mr. Musk, who began criticizing FEMA for spending its money to house illegal immigrants rather than help hurricane survivors. “Kamala spent all her FEMA money, billions of dollars, on housing for illegal migrants,” Mr. Trump claimed at a rally soon after the storm, referring to Kamala Harris, then the vice president and his rival in the presidential race. Mr. Trump appeared to be referring to the Shelter and Services Program. Congress approved it under the Biden administration, directing FEMA to run a program for housing migrants who entered the United States and were released by federal officials. Congress gave the program $650 million last year for cities, states and nonprofits, but Mr. Trump’s comments were inaccurate. FEMA’s spending on migrants does not mean FEMA has less money to spend on disaster survivors. The money for migrants comes from the budget of Customs and Border Protection, not out of FEMA’s budget. Money for disaster survivors comes directly from Congress. There is no overlap between those two funds. Soon after his return to the White House, Mr. Trump made Mr. Hamilton acting FEMA director. A former Navy SEAL and congressional candidate who campaigned on an anti-illegal immigration message, Mr. Hamilton did not have experience running a state or local emergency management agency. DOGE members arrived at the agency’s downtown Washington headquarters in early February to begin going through contract and grant payments. Then came Mr. Musk’s post. “The @DOGE team just discovered that FEMA sent $59M LAST WEEK to luxury hotels in New York City to house illegal migrants,” Mr. Musk wrote, exaggerating the quality of hotel rooms that were used. He added that FEMA had in his view violated an executive order from Mr. Trump, which ordered the agency to pause money supporting undocumented migrants. “A clawback demand will be made today to recoup those funds,” he wrote.