Threads' contexts should be independent from each other. If reading your stack trace relies on the state of other threads, you've got a very brittle design.
What is lost is the history of the state the current thread is working with, but the state should be fully encapsulated within the thread, except in the case of large shared read-only input buffers that are being processed in parallel. But those latter buffers aren't hidden from the current thread nor its debugging. Debug information can also be logged on state objects to show its provenance.