BEIRUT — With its stockpile of food dwindling rapidly and government forces tightening their stranglehold on rebel-held eastern Aleppo, the Khattab family dreads what could come next. The brutal blockade has brought the family’s side of the city close to starvation, while punishing airstrikes have turned trips to local markets into life-or-death excursions.

Over the weekend, Syrian President Bashar al-Assad’s forces made major advances against the remaining rebel enclaves, but even as thousands of residents flee, many others are refusing to leave, fearing capture.

Those who are staying have very little left after years of war and months of a near-total blockade.

“We’re only eating two small meals a day now, and it’s just rice and cracked wheat,” said Moataz Khattab, 26, who lives with nine family members. “We eat together, what we can, but we are losing so much weight. We’re running out of supplies, and now we talk about starving to death.”

Since Sunday, rebel defenses in Aleppo — divided since 2012 between rebels in the east and government-held districts in the west — have started unraveling. Government forces have seized more than a third of the east, prompting more than 16,000 people to leave the area, according to Stephen O’Brien, the U.N. humanitarian chief.

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