CYA is "Cover Your A**" where A** is a 3-letter term for your posterior. CYA occurs, for example, when you write a memo for the record pointing out the dangers of a proposed course of action so that everyone understands the risks. For example, "Although Ms. Jones appears rehabilitated, there is intrinsic risk in hiring a convicted poisoner as a personal chef." Sometimes protecting yourself (CYA) is what you need to do, but it can be carried to extremes.
As a practical matter, it often means documenting things so you can demonstrate that you notified others of things they need to know and it becomes the recipient's responsibility to do something with it.
For example, I work in a Tax Department. I send an email to the Account Administrator saying that we're going to take $10,000 out of account XYZ on December 28th to make an estimated tax payment, and they need to make sure that sufficient funds are available to make that payment. If we make the payment and the account becomes overdrawn, it's the Administator's responsibility. My email to them was a "CYA," which I can produce (and save my rear) if the Administrator claims no one ever told them that this payment was to be made.
The unfortunate thing about CYA's is that with such a litigious and competitive society, it's not uncommon now for people to copy "the world" on emails as a form of CYA. This can make it very difficult for the recipients to determine if it's their responsibility, and can lead to more emails being sent for others to "CYA."
I believe the above posts explained the concept of a CYA very succinctly, anthough I never bother with CYA emails myself.
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