At age 9, Mr. deBrum was fishing with his grandfather when he saw the flash of one of the tests on the horizon. “Within seconds, the entire sky had turned red, like a fishbowl had been put over my head, and blood poured over it,” he recalled.

The deal offered: an open door to the Marshallese and Bikini Islanders. That bargain has already fostered communities of thousands of Marshall Islanders in Springdale, Ark., and Salem, Ore., fleeing a deluged future. That 1986 compact also established a United States government fund to support Bikini Islanders — as long as they continued to live in the Marshall Islands. Now the Bikini Islanders want to use that fund to move to the United States.