In some cases a one-way request without a response can be fired to a TCP server, without a SSL certificate. A TCP server, in contrast to a HTTP server, will catch you request. However there will be no access to any data sent from the browser, because the browser will not send any data without a positive certificate check. And in special cases even a bare TCP signal without any data is enough to execute some tasks. For example for an IoT device within a LAN to start a connection to an external service. Link
This is a kind of a "Wake Up" trigger, that works on a port without any security.
In case a response is needed, this can be implemented using a secured public https server, which can send the needed data back to the browser using e.g. Websockets.