In California, UDs are subject to restricted access for 60 days. You don't give enough information for a thorough answer on whether the UD will be public; however, California Code of Civil Procedure section 1161.2 outlines the restricted access provisions.
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Keep in mind that it is pretty easy to find any kind of lawsuit that is filed against you because lawsuits are public records. There are very cheap and easy to use databases that can locate lawsuits of any sort filed against you. Depending on the kind of background check being used, it may or may not show up.
Good luck to you.
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I agree with my colleague that, unless ordered otherwise, a UD is unmasked after 60 days and will become a matter of public record. Whether a UD will show up on a background check prior to expiration of the 60 day period is anyone's guess. It depends on the thoroughness of the check and whether it includes non-public sources such as interviews with your friends and associates, including your landlords, and non-public commercial sources such as data bases compiled by landlords.
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