Declares that this consumer renders a per-task stop control wired to the `stop_task` control request, so the user can stop an individual background task. When declared, an interrupt on an open-input (interactive stream-json) session spares running background agents/workflows (Stop only aborts the turn). Closed-input exception: a one-shot run (string prompt / -p closes stdin) still kills hold-back tasks at the held-result release regardless of the declaration — with stdin closed, a stop_task control could never be delivered, so the fail-closed kill stands. ABSENCE also fails closed: the interrupt kills background tasks, since the user would otherwise have no way to stop a runaway one. First-attached-client-wins on multi-client sessions; later initializes do not change it.