I understand why you're searching for a sample. The stakes of this letter feel too high to freelance: one shot, maybe, at a mother or a brother or a daughter who might read the first two lines and stop. So you want a proven script, something field tested, and the internet obliges with templates full of phrases like "I deeply regret the circumstances that led to our estrangement."
Here's the problem, and it's fatal: the person receiving this letter knows your voice. They've known it their whole life. A reconciliation letter has exactly one asset, which is that it proves you, specifically, sat down and meant something, and a template burns that asset in the first paragraph. The moment your mother hits a sentence that doesn't sound like you, the letter stops being a hand extended and becomes a document, and people don't reconcile with documents.
So no sample. Instead, the structure that every good version of this letter shares, five parts, with the understanding that you supply every actual sentence.
Open with why now. Not the history, the reason this letter exists today. "I turned fifty last month and you weren't there, and I couldn't stop thinking about it." One or two lines, concrete, yours. This earns the read, because it answers the question every estranged recipient asks first: why is this arriving now, and is it real.
Own your side without a ledger. Somewhere in the middle belongs the hardest paragraph, the one where you name what you did or failed to do, in plain words, without attaching the matching list of what they did. Not because their side doesn't exist, but because a letter that says "I'm sorry for X, but you also" is an invoice, and invoices get disputed, not answered. If your honest accounting is that the fault runs heavily their way, the letter can still own something true: "I let years go by without trying. That part is mine."
Say what you're not asking for. This is the paragraph the templates never include and the one that most changes how the letter is received. "I'm not asking you to pretend nothing happened. I'm not even asking you to respond." Estranged people brace for demands the moment they see your name. Removing the demand, explicitly, on paper, is what lets them keep reading with their shoulders down.
Make one small, concrete, refusable offer. Not "I want us to be a family again," which is enormous and unactionable. Something a person could actually say yes to: "If you were ever open to a phone call, or even letters for a while, I'd like that." Small enough to accept, clearly okay to decline.
Close without a hook. No "I'll be waiting to hear from you," which converts the whole letter into pressure. Something that stands whether or not a reply ever comes: "Whatever you decide, I'm glad I finally said this."
Then the part nobody wants to hear: write it, put it away for a week, and reread it as them. Every line that sounds like a lawyer, a therapist, or a stranger, rewrite in the words you'd use out loud. The letter doesn't need to be eloquent. Eloquence is what the templates sell, and it's the wrong product. It needs to be unmistakably, sometimes clumsily, you. Clumsy and true beats polished and generic in this genre every single time, because true is the entire message.