Does this mean that some types never get resolved? How does the type checker handle that?

Indeed, the link gives an example of such an infinitely recursive type:

    type Foo<T extends "true", B> = { "true": Foo<T, Foo<T, B>> }[T];
    let f: Foo<"true", {}> = null!;

As for how it's handled, it yields the error "Type instantiation is excessively deep and possibly infinite. [2589]" I'm not sure what the max stack depth is, though.