New York, Aug. 28 -- For Shashidharan Sreedharan, the last message from his wife and daughter arrived at 10 pm New York time. By the next morning, the road they were due to travel had disappeared under mud and water.

Rekha and Rashi Shashidharan had just completed their pilgrimage to Mount Kailash, the peak revered by Hindus and Buddhists as the abode of Lord Shiva. They were expected to cross back into Nepal at noon on Wednesday. Instead, a suspected glacier collapse in the mountains above sent a flash flood tearing through the Rasuwa district on the Nepal-Tibet border, a disaster so violent that seismic monitors briefly registered it as an earthquake.

Amid the unfolding humanitarian crisis, families back home are enduring an agonising...