SAN DIEGO — Migrants who are allowed to remain in the United States to pursue asylum are usually given a choice when they are released from detention in San Diego: Go to the Greyhound bus station and fend for themselves, or try to find a cot and a shower at a local shelter.

One way or another, once the migrants have been dropped off by discreet white Immigration and Customs Enforcement vans in border towns across the Southwest, they are no longer the federal government’s problem.

President Trump has tried and failed to end a practice he derisively calls “catch and release,” and thousands of undocumented migrants apprehended at the border every month are still being granted routine entry to the United States while their cases are processed by immigration courts.

But as the number of migrant families in recent months has overwhelmed the government’s detention facilities, the Trump administration has drastically reduced its efforts to ensure the migrants’ safety after they are released. People working along the border say an ever larger number of families are being released with nowhere to stay, no money, no food and no means of getting to friends and relatives who may be hundreds or thousands of miles away.