Free indirect discourse is a type of narrative device which has some similarities with direct discourse and some with ordinary indirect discourse, but is different from both. Here's an English example, from Joyce's Portrait of the Artist as a Young Man:
The muddy streets were gay. He strode homeward, conscious of an invisible grace pervading and making light his limbs. In spite of all he had done it. He had confessed and God had pardoned him. His soul was made fair and holy once more, holy and happy. It would be beautiful to die if God so willed. It was beautiful to live in grace a life of peace and virtue and forbearance with others.
The first two sentences are regular narration, but starting with In spite of all he had done it, we're in free indirect discourse. That sentence and the following ones no longer represent the narrator's thoughts but the character's; but they're neither direct discourse (Stephen thought, "In spite of all I have done it") nor standard indirect discourse (Stephen thought that in spite of all he had done it). Basically, it's indirect discourse without a verb of speech or thought acting to introduce it. The grammatical transformations of indirect discourse still apply (change of tense, change of grammatical person), but there's no he thought that..., she said that..., or anything else to show that the narrative has switched viewpoints.
In Latin and Greek, we're all familiar with the rules of standard indirect discourse, but I don't recall ever hearing about free indirect discourse in these languages; in fact, FID is generally thought of as a specifically modern literary device. Is there anything comparable to FID in these languages?
An obvious answer might be that in Latin, indirect speech goes into the accusative and infinitive, and it's very common to find that construction without an overt verb of speech: just a sentence in ACI, where the reader is expected to mentally fill in the they said (there's lots of this in Caesar, Livy etc.). So if FID is defined as indirect discourse without a verb of speech, the answer is clearly yes. But this strikes me as different from what's happening in the passage above: there, nothing in the grammar signals the passage from narration into indirect discourse, as ACI does in Latin. "Proper" FID in Latin, if it exists, would simply continue the narrative with regular finite clauses, but with an implied change of viewpoint into the consciousness of a character. Does anything like this exist in Latin or Greek?