How would you remember a random string if you cannot remember a subject line (or even body text) worded by a human? All email clients allow you to search the subject, body, presence/absence of attachments, from, to, etc. Message-ID, References, In-Reply-To...there are already several headers created and managed (though in a hidden way) by email clients. But the values of these headers are usually long strings that humans cannot easily remember.
Open up an emails from different email threads (preferably one that has been sent later in the reply chain) and see the raw headers. There's a lot of information there. Something in it could be useful to you or for you to devise something better than the status quo.