For the long running scenario, why not use Links? The specification describes[1] a similar scenario and how links can be leveraged to causally relate spans even across trace boundaries.

As for the crashing scenario, this seems like an application-level concern. Ideally it is not waiting until the crash to send traces. Depending on the environment, the application could handle the crash and deliver the telemetry leading up to it before shutting down.

[1]: https://github.com/open-telemetry/opentelemetry-specificatio...