Subrequests in an KernelEvents::TERMINATE event subscriber (f.e. cron tasks doing subrequests) try to restart a session, resulting in runtime exceptions

When cron runs, I get this runtime exception every time, but with various referrers. Most of the cron sessions work fine:

RuntimeException: Failed to start the session because headers have already been sent by "/home1/suppotf0/public_html/core/modules/big_pipe/src/Render/BigPipe.php" at line 264. in Symfony\Component\HttpFoundation\Session\Storage\NativeSessionStorage->start() (line 135 of /home1/suppotf0/public_html/vendor/symfony/http-foundation/Session/Storage/NativeSessionStorage.php).