«Я поздно встал — и на дороге.
Застигнут ночью Рима был!»
It means "Too long I slumbered, and Rome's night // Has overtaken me upon my journey!"
This is a paraphrase of this excerpt from Cicero's "Brutus":
I must own, however, though I am heartily grieved that I entered so late upon the road of life, as to be overtaken by a gloomy night of public distress, before I had finished my journey
Я поздно встал — и на дороге застигнули ночью Рима!
This is barely grammatical. I can probably imagine a context where it would make sense, but that's not how people speak and, in any case, that's not what the poem means.
If you want to use an active construct, you could use я поздно встал, и на дороге меня застигла ночь Рима.
What is this construction? How to generalize? Why is был in the singular (what is the subject?!) while застигнут is in the plural?
Я был застигнут ночью Рима means "I was overtaken by Rome's night". Ночью here is not an adverb, it's a noun and the agent in the sentence. Я is the subject (and a patient, since the sentence is passive).