The three of them went back home, hungry and tired.
"hungry" and "tired" are adjectives. You could rephrase: They went back home and they were hungry and tired.
They are hungry and tired, not the way of their going.
I don't know which terms are used in English grammars for this use of adjectives, probably more than one. I think in Latin grammar this use is called Prädikativum, at least in my Latin grammar.
I tried to find what term is used in my English grammars for this use, but it seems that it is not registered at all. I looked through
Oxford Guide to English Grammar by John Eastwood
Longman English Grammar by L. G. Alexander.
Generally speaking, there are a lot of cases where a verb is not followed by an adverb but an adjective. But this is a grammar chapter that is often neglected in grammars. Some examples:
to travel light, to speak true, to arrive safe and sound, to talk big, to get off light, passion ran high, imagination gone wild, to drop dead, A new broom sweeps clean, etc.