One example would be a search field that shows suggestions from the server while typing.
The Stackblitz example is quite good too.
I'll give it shot to build a super simple one with just vanilla JS without helper libraries like Lit or Stencil. I think I'd take the same approach as I would with React, and I think the biggest difference would be where the fetch gets executed. In React you'd expose a prop like "submitHandler", but here I would emit an event from the component (after whatever debounce amount) and expect the caller to attach an event listener to my custom event to perform the fetch.