Struggling to find basic staples in her own country, Mariana Revilla and five neighbors here took to crossing a treacherous 60-mile gulf under the cover of night to the island of Trinidad.

On her last trip, they made a good haul, securing seven tons of flour, sugar and cooking oil from the former British colony in exchange for fresh shrimp from home. But on the way back their rickety 46-foot boat capsized, leaving Ms. Revilla and her companions clinging to the wreckage for nearly two days before she and two others ran out of strength and drowned, according to survivors. Her stepfather says her 3-year-old daughter, Isabel, keeps asking, “Where is my mama?”

As Venezuela’s economy crumbles, an increasingly desperate people are doing all they can to get food and medicine. Here that can involve great peril.

Venezuelans make trips as long as 10 hours to hawk shellfish, plastic chairs, house doors, ceramic pots and even exotic animals like iguanas and brightly feathered macaws. They are exchanged for basic goods—rice, detergent, diapers—that Caracas is increasingly unable to provide.

“It’s thanks to Trinidad that we have any food here,” said 49-year-old Angela Caballero, a resident of this town on a peninsula that extends toward the island. “If that didn’t come, we’d be dead.”