make a script to encoding with ffmpeg even if the input stream fail.

I need to continue encoding with a black background even if the source fail. The issue is that ffmpeg pause encoding when any input as no new data. It restarts only when the source is reactivated, but the output stream is now broken. I need a solution to force ffmpeg to continue encoding even if one stream input has no data for a short amount of time. Black screen, alternate stream, last frame repeated. I need to continue encoding at 30 fps.