You should never admit fault if an insurance company reaches out to you in the aftermath of an accident or injury. It is not up to you to determine whether you were at fault or partly at fault for an accident.
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That said, even if it is determined you were partly at fault for an accident, New York State and many other jurisdictions have a legal system that recognizes “comparative negligence” or “contributory negligence.” That means that even if you were partly at fault, you can still receive a large percentage of a settlement.