diff --git a/src/stats.c b/src/stats.c
index ac36ebe0a..5379332ca 100644
--- a/src/stats.c
+++ b/src/stats.c
@@ -4316,7 +4316,18 @@ static void http_stats_io_handler(struct appctx *appctx)
 	}
 
 	if (appctx->st0 == STAT_HTTP_DONE) {
-		/* no more data are expected. Don't add TLR because mux-h1 will take care of it */
+		/* no more data are expected. If the response buffer is empty,
+		 * be sure to add something (EOT block in this case) to have
+		 * something to send. It is important to be sure the EOM flags
+		 * will be handled by the endpoint.
+		 */
+		if (htx_is_empty(res_htx)) {
+			if (!htx_add_endof(res_htx, HTX_BLK_EOT)) {
+				si_rx_room_blk(si);
+				goto out;
+			}
+			channel_add_input(res, 1);
+		}
 		res_htx->flags |= HTX_FL_EOM;
 		si->cs->flags |= CS_FL_EOI;
 		res->flags |= CF_EOI;