I believe the traditional example is a spacecraft passing over the cosmological horizon. We cannot observe this spacecraft, so the belief "things passing over the cosmological horizon cease to exist" cannot be experimentally proved or disproved.

However, the conclusion that they don't subjectively cease to exist after we can no longer communicate with them follows unambiguously from the well-tested models of physics and cosmology. It does not require any strong extra assumptions, only some very weak ones, like that we are not in a cosmic-scale Truman show, or that the Copernican Principle holds.

By comparison, many-worlds is a strong extra assumption which has never been tested and is currently not testable (no, despite the popular misconception here, it does not follow from "just" the Schrodinger equation).