First, separate the message from your need to send it
When someone shuts you out, most of the urge to reach them is about your own discomfort, not their need to hear from you. That is worth naming honestly before you do anything, because a message driven by your discomfort will land as pressure no matter how carefully you word it.
There is a smaller set of messages that genuinely belong to the other person: information they are entitled to, an apology they are owed, a goodbye that history calls for. Those can be worth sending even into silence. The test is whether the message would still be worth sending if you knew for certain they would never reply.
Lead with the fact, not the feeling
If there is real information, a diagnosis, a birth, a death, a hereditary condition they should know about, a legal or financial fact, lead with it in the first line. Facts are far easier to accept from someone you are avoiding than feelings are.
If there is no fact and the message is purely emotional, it is almost certainly an apology or a goodbye. Both are legitimate. Neither should carry a question or a request attached, because a request is the thing they shut the door to avoid.
Say it once, and mean once
The single most common reason people refuse to read a message from someone they have cut off is the reasonable fear that reading it restarts a cycle they already had to end. A follow up asking if they saw it, a second attempt on another app, a message to a mutual friend, each one confirms that fear and undoes whatever the first message might have done.
So decide before you send that this is the entire attempt. One message. No sequel. Keeping that promise is what makes the message trustworthy in the first place.
Do not reach them through the back door
If they have blocked you, resist the workarounds. A new number, a hidden caller ID, a fresh account, or a friend passing it along all reach them by removing their ability to refuse, and that is exactly what makes a hard situation into a frightening one. It also converts a private matter into something that can look like harassment from the outside.
The delivery has to respect the person as much as the words do. A message that arrives unannounced, forcing them to engage just to find out who it is from, is a demand. A message that announces itself and can be deleted without a word is a request.
The honest way to deliver one message
An announced, refusable request is built for exactly this. They see that someone is asking and that it cost you something real, and they choose whether to open it. If they never do, you still said the thing once, properly, and left them free to refuse. That is what respecting someone looks like when they will not talk to you.
If your situation is more specific, we have written it up in detail: how to apologize to someone who won't talk to you, what to say after a breakup when they have stopped replying, and how to reach out to an estranged parent, sibling or child. Start with the one that fits, then say your piece once.