What if she got caught in a fishing net and washed up on shore in Mayumi's secret spot? A spot that Mayumi found when she was just a child. It's basically isolated from the rest of the beach and you have to climb over a lot of sharp rocks to get to it.

So I have in mind that Mayumi lives in a small fishing town, that has a really nice beach all around the land. I'm thinking maybe they even live on an island and have to use a ferry to go to the mainland and such.