It depends on how much of a character that person has built as a liar. If they are just a pathological liar, then nobody will ever believe them. It's like the boy that cried wolf. They all believed him for the first few times, but when it actually happened, nobody believed him because he was lying so much. Nobody believes a liar, even if they are telling the truth, because that is the kind of character that the liar built for themselves.