A stream is considered "active" when it is alive. That means, it exists. There is a special transition state (active->enqueuedForDelete->deleted). So, listStreams only lists those.
If the counters are stalling on an output stream that means the output stream lost its link with the input stream. Depending on the technology used (RTMP or RTSP), the whole connection may be brought down: RTSP connection is brought down, RTMP connection is maintained because the input may come around again, and RTMP has built in support for resuming