What do tax havens like the Cayman Islands get from storing other people's money?

So let’s say you’re a rich celebrity. You decide to move all your money from US banks to the Caymans so you don’t have to pay taxes. Maybe you even change your citizenship to there. They happily take your money and store it in one of their underground sugar mines. Then what? Out of the goodness of their heart, they agree to be a target of governments trying to sue or pressure them into giving up the info on who has what stored?

I’m assuming that places such as these don’t have taxes so that’s why people move their money there. So why would they do that? Surely get they something.

The Cayman Island has a substantial banking industry to manage all of the offshore money stored there, which provides direct and indirect employment. I don’t see a reason why there’d be a major banking sector on a tiny island in the Caribbean otherwise.

Well surely they would not do something so foolish as to make loans which produce interest like most banks do the world over.

Banks don’t make money by storing cash, they lend out money and charge interest on it. They pass some of that interest on to you. They probably also pay taxes on their profits to the Cayman Islands. The Caymans benefit from this, and also from the employment the banks provide.