The barrage of tornadoes that tore through six states killed at least 74 people in Kentucky, officials said on Monday, as those fortunate enough to survive unscathed opened their doors to victims whose homes were destroyed, and hundreds of the suddenly homeless took refuge in shelters.

The death toll was likely to rise as 109 people remained missing, Kentucky Governor Andy Beshear said. Some 28,000 Kentucky homes and businesses still lacked power. The tornadoes, which the governor estimated damaged or destroyed 1,000 homes, surprised people by striking unusually late in the year during cold weather on Friday.

The dead, including at least...