diff --git a/src/mux_h2.c b/src/mux_h2.c
index 336bd4e0f..c91905f92 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -2622,6 +2622,7 @@ static void h2_detach(struct conn_stream *cs)
 	    ((h2c->conn->flags & CO_FL_ERROR) ||    /* errors close immediately */
 	     (h2c->st0 >= H2_CS_ERROR && !h2c->task) || /* a timeout stroke earlier */
 	     (h2c->flags & (H2_CF_GOAWAY_FAILED | H2_CF_GOAWAY_SENT)) ||
+	     (!(h2c->conn->owner)) || /* Nobody's left to take care of the connection, drop it now */
 	     (!b_data(&h2c->mbuf) &&  /* mux buffer empty, also process clean events below */
 	      (conn_xprt_read0_pending(h2c->conn) ||
 	       (h2c->last_sid >= 0 && h2c->max_id >= h2c->last_sid))))) {