HAMDAYET, Sudan — The refugees were hungry and exhausted, their shoes dusty and worn from trudging for four days through the bush and forest of northwestern Ethiopia, hiding from soldiers, as they escaped the conflict in the country’s Tigray region.

Finally, they made it safely to the small Sudanese border town of Hamdayet. But they had nowhere to sleep and nothing to eat. So they sat in a sandy alley close to the center of town, asking passers-by for food and water.