The government did not just stand aside, it often undermined aid. Donated supplies went undelivered. Small grants required signatures from the prime minster. During a fierce snowstorm, security forces blocked delivery of tents until a cabinet member intervened.

“Our government worried too much about politics,” said Emad Shoumari, mayor of a majority-Sunni town, Marj, that has embraced refugees. “This kept the refugees from getting the aid they needed.”

What really makes refugees politically radioactive is a painful national memory. Palestinians poured into Lebanon in 1948 and 1967, fleeing conflicts with Israel. Their arrival stoked sectarian divisions that helped ignite civil war. More than 400,000 Palestinians still live here, in camps with pockets of poverty and extremism where violence periodically erupts.

Bowing to fears of another destabilizing influx, the government ruled out camps for Syrians, provided limited help and gave international agencies little leeway. United Nations officials made the best of it, saying, perhaps wishfully, that at least refugees would be integrated into society. No one greeted Syrians at the border. Some joined relatives among 500,000 Syrian laborers already here. Others had no idea where to go, and followed word of mouth.

One of the warmest welcomes was in Saidnayel, the Sunni town in the central Bekaa, where the flag of the Syrian revolution flies openly. A year ago, it hosted 265 refugee families, their names recorded in a handwritten ledger.

“When they reach the borders, they ask for directions to Saidnayel,” the mayor, Mr. Shubassi, said proudly then. “Each Friday we protest against the Syrian regime.”

He squeezed one family into a bakery, others into a row of storage rooms. The Syrian Army was bombarding cities, and the mayor expected “an avalanche.”