In Island of the Blue Dolphins, what is the solution to the problem: Karana is acidentally left behind when her people leave her island.
Karana is not really left behind accidentally; it is her brother, Ramo, who is left when the ship sails. Karana is told they cannot go back for him because the tides have made it dangerous to return at that time. Although she is assured her people will return for Ramo soon, and that he can survive for a short time by himself, she dives off the ship and swims back to the island to protect him.
Unfortunately, she cannot. Within a few days, Ramo is killed by a pack of wild dogs. Karana is then left to survive by herself. It is not clear how long this time will be, but it turns out to be 18 years. The "problem" of Karana's abandonment is not really solved. Rather, she learns to get along on her own, befriending first one of the wild dogs, some wild birds she tames, and then a sea otter pup that she raises after it has been wounded by Aleut hunters.
Over the course of her many years on the Island of the Blue Dolphins, Karana develops a close bond with the natural world. We read, "After that summer, after being friends with Won-a-nee and her young, I never killed another otter...Nor did I ever kill another cormorant...Nor did I kill seals for their sinew."
She tells us, "...animals and birds are like people, too...Without them, the earth would be an unhappy place."
Like the real Lost Woman of San Nicolas on whom the story is based, Karana is eventually "rescued" from the island and brought to a mission in Santa Barbara.