Dear {Name},
I feel like I need to put this down in writing to really drive it home. What happened is not your fault. I am the one who {caused issue/committed act/etc.} You are completely blameless, and I will do everything I can to make sure that people know that.
I am so, so sorry about what happened. In retrospect, I would have {different action}. I regret that this has blown back on you in any way whatsoever. You don't deserve it; I do.
Please let me know if there is anything I can do, or anyone I should reach out to, to further get the message out that what happened is not your fault.
Sincerely,
{Name}
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