I highly recommend you discuss your situation with a New York litigation attorney (if you do not have one) in a confidential forum as soon as possible as there may have been a Default Judgment granted against you. You may still have time to file a Motion to Vacate Default Judgment, but the allowed time is running and may have already expired.
Notify your insurance carrier immediately. You can make an application to the court to vacate the default judgment, but you need to make your insurance company aware or they may disclaim any liability to pay.
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You were allegedly served and defaulted. You can move to vacate the judgment, ask for a traverse hearing, etc. However, you should obtain a copy of the court file first and then meet with a lawyer, since s/he will have to review the affidavit of service and perform a legal autopsy and hopefully breathe new life into your case.
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Dear Property owner:
No lawsuit is allowed to proceed to a judgment by default without the court reviewing the plaintiff's proof that service of the summons and complaint was made as required by law. That does not mean that a process server may not fib in the affidavit of service, but does answer your concern about how this could happen. New York courts have multiple layers of requirements before allowing a matter to proceed to a default. An hearing in your absence ( an inquest) may have occurred.
With an owner having direct liability for all injuries occurring on the property including the sidewalk, you either insure or you become your own insurance company. Unless you are fantastically wealthy self-insurance is an easy route to losing your property to a stranger who happens to fall or claims to fall on the sidewalk at your property.
You need a lawyer. If the default occurred over one year ago there may be serious time issues involved but in any case you no longer have time to chat about this serious matter in an online forum, you need an attorney, now.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.