The ultimate fate of the Arawak Indians was to die out. They were killed off by a variety of factors that were connected to the coming of the Spaniards to the New World.
In Chapter 1 of this book, Zinn is trying to emphasize the idea that Columbus was not really a very good person and that we should think of him as someone who was guilty of genocide. Zinn starts the chapter out by talking about how good the Arawak people were. He argues that they were generous and friendly. He is trying to contrast this with the greed and the desire to dominate others that the Spanish felt.
Zinn emphasizes this because it is important to him to point out that these gentle people were utterly destroyed by the coming of the Spanish. Therefore, he tells us that the Arawaks died out completely. He says
A report of the year 1650 shows none of the original Arawaks or their descendants left on the island.