I'll start by saying, that i don't know, if there was ever a case like you described with Herodotus and Claudius.

However, if you take a look at ancient literature and how it works, it seems unlikely. I will explain that second. First, you can see a vague idea of "intellectual property" by looking for example at Vergil's Georgics, where he says.

So sang I of the tilth of furrowed fields, Of flocks and trees, while Caesar's majesty Launched forth the levin-bolts of war by deep Euphrates, and bare rule o'er willing folk Though vanquished, and essayed the heights of heaven. I Virgil then, of sweet Parthenope The nursling, wooed the flowery walks of peace Inglorious, who erst trilled for shepherd-wights The wanton ditty, and sang in saucy youth Thee, Tityrus, 'neath the spreading beech tree's shade. [Vergil. Bucolics, Aeneid, and Georgics Of Vergil. J. B. Greenough. Boston. Ginn & Co. 1900.]

This part serves as identification. It states who wrote the above: Vergil. It states when it was wrote (vague) by telling us the place Augustus (Caesar) was fighting at the time (even if you can't tell the exact year by reading this alone, you should be able to tell that it can't be e.g. 250BC). Further it is specified that the Vergil, who wrote this, is the same Vergil, who wrote the Bucolics by refering to the first eclogue (Tityrus and the beech tree). But as i said in the beginning, this is a vague idea of "intellectual property". It neither is an assurance, that the whole opus is solely based on ideas of Vergil, nor does it mean, that it would be necessary for a later author to testify, where he got his information, if he recites it or uses its contextual ideas. The reason for that is, as implied at the beginning, that ancient (Roman) literature works on another level than we are used to it.

If you take a look at Roman literature you will always discover parallels to other authors and their works. These parallels can reach from subjects to literal adoption, but usually combines more aspects. In simple words: An author shows his talent by adopting words, phrases and/or subjects from previous works of other authors. Staying with the example of the georgics, you can see that Vergil uses words and sentence structure previously found by Lucretius (among others). That doesn't mean, that vergil tries to steal the "intellectual property" of Lucretius. He rrather plays with it. He describes a pest in the 3rd book of his Georgics in a similiar way to how Lucretius describes a pest in his De Rerum Natura. Now this works on three levels:

1. Vergil shows his knowledge of Lucretius
2. Vergil aknowledges Lucretius' work on the same subject
3. Vergil plays with his readers, by giving them the chance to test their own knowledge identifying Lucretian language

The last aspect is important to my assumption, that is really unlikely someone would be able to just plain copy a work of another author in antiquity using his own name. Judging by the giant amount of connections between ancient texts it seems almost certain, that ancient readers were really versed in ancient texts (they knew their shit). So if your Claudius was to publish his exact copy of Herodotus, you can be sure most reader would have been able to identify this as the work of Herodotus (since he was well known anyway) and it is unlikely that a plain copy would be accepted, since it shows no literary skills.

As an example how to imagine it: If any show or movie these day references "with great power comes great responsibility" you will most likely think of Spiderman as the author. Ancient literature works like this, but to some extent more complex.

If you are interested in this subject there are several ways you can explore it. You could just take an ancient text, that you are interested in, and read it following up by reading a commentary on that text. That can be done for free with (some/most) texts and commentary via Perseus Collection. (Attention: old english! - not always that easy). It could be done with newer commentaries and translations, but especially the commentaries are really expensive. It could also be done by introductions to ancient literature like Conte's "Latin Literature. A History" (i hope i remember this right).

TL;DR Ancient literature works on references and recitation resulting in copying of subjects, phrases and words. The readers apparently enjoyed and identified those cases. A plain copy of an existing work published by a new author seems unlikely due to that habit.

P.S. English isn't my native language. Syntax and commata might be somewhat wild.