What is the fallacy called where "Nothing a liar said can be true" (i.e., "false in most things, false in everything")?
For example, consider that 99% of something someone said is false, but 1% of the time, they speak the truth. As a result, it is argued that the 1% of truth is actually false (and cannot be accepted - even from a non-liar) because it came out of the mouth of the liar.
"X said Y, therefore Z", e.g. "Lying Laura said it will rain, therefore Truthful Tom's claim that it will rain is false," is a fallacy of origins, AKA the genetic fallacy, AKA the fallacy of virtue.
"Y is associated with X, therefore everything associated with X is part of Y", e.g. "Lying Laura lies, therefore agreeing with Laura about the weather makes Truthful Tom a liar," is a fallacy of association.
A Roman legal doctrine, falsus in uno, falsus in omnibus (false in one, false in all). Essentially a warning to not accept the testimony of a witness who has lied (even once) wthout corroboration. There's no fallacy because all its saying is to be extra cautious with known liars and their words. This amounts to seeking alternative confirmatory evidence (e.g. by checking whether other witnesses also concur).
If it is a fallacy, then uno (one) is a really, really, really poor sample i.e. statistically the fallacy of hasty/sweeping generalization. It could also be called The Boy who cried wolf fallacy (the boy, when he did tell the truth, was not believed).
False dilemma.
It argues that a person either tells the truth or tells lies, and ignores the third route of telling a mix.
However, "false in one thing, false in everything" is a legal axiom, and rests on the psychological fact that a person willing to lie is often willing to lie on many things, and is untrustworthy.
If you reject an argument solely because the person who promoted the argument is a known liar, this is the genetic fallacy. It's where you judge an argument based on its origins rather than its merits. It is fallacious because there's nothing preventing a liar from making a good argument, even if by accident ("even a stopped clock is right twice a day"). https://www.scribbr.com/fallacies/genetic-fallacy/
However, in this case you're not describing an argument that can be judged on its own merits, you're describing claims of fact. Obviously a claim of fact will be either true or false, regardless of who says it (there are no "perfect liars" in real life). But if you don't have any independent way to judge its truthfulness, you'd be justified in treating it with suspicion, if you knew that its source was unreliable. You wouldn't be able to be sure it was false, you just wouldn't have any strong reasons for believing it to be true.
Something similar has been called the Fallacy Fallacy. Where you assume an argument that contains a fallacy has an untrue conclusion. For example:
Alice: "Dogs have 4 legs. Therefore the sky is blue."
Bob: "That's a fallacy! Therefore the sky is not blue."
I suspect this is really a corruption of the principle that nothing a liar says can be trusted.
To label someone a liar is to say that their utterances are known to be untrustworthy and their intention known to be manipulative - that it will never be apparent to the listener whether the liar is telling the truth or is practising to deceive.
The status of being a liar is accrued by their being merely inconsistent in telling the truth and using information to manipulate, not by their every word being false.
It is rarely the case that a liar always declares false information, such that the truth could be inferred by merely interpreting the opposite of the information conveyed by the liar.
From such a ridiculous status point, the liar could always increase the manipulation, and break the ability to infer the truth, by occasionally telling the truth.
