(() => {
  // A class instance whose `toJSON()` throws renders as unconvertible, the
  // class name included in the loss.
  class Throws {
    toJSON() {
      throw new Error("nope");
    }
  }
  return { instance: new Throws() };
})()

--

instance:
/unconvertible("nope")
/unconvertible("nope")
{
  "/unconvertible": "nope"
}