Hmm.
Let’s focus on the rest of the sentence before we focus on “come home” so that, once we analyze “come home,” we will better be able to understand its relation to the rest of the sentence.
I – subject of the sentence
heard – verb sentence
I heard.
I heard what/whom?
I heard him.
him – object of “heard”
I heard him how/when?
I heard him late.
late – adverb
Elliptical infinitives are when the “to” is dropped from an infinitive. Let’s look at some examples and see if “come” could be an elliptical infinitive.
The use of a simple infinitive can be observed in the sentence, “My goal is to achieve greatness.”
The “to” is typically dropped in cases that would make the sentence ambiguous and before verbs like bid, dare, help, let, make, need, and see.
An example of the to being dropped when it would make the sentence ambiguous is, “All he did was _ succeed at everything he tried.” “to” is dropped before succeed because, otherwise, the sentence could mean that he did everything he did in order to succeed.
I do not believe this to be an example of this case. “I heard him to come home late” is not logical.
Let’s think of another verb after “him” in a more simple sentence. “I heard him yell.”
What is yell in that case? I heard him do what? I heard him yell.
I am not sure what “yell” would be called in this instance, but whatever “yell” would be called, “come” functions as the same thing.
I then believe that “home” is something that is modifying “come” because it answers the question “where” he comes.
(One year ago, I totally would have been able to answer this better… I was a grammar terminology queen… Having been away from tutoring grammar for a year, I have apparently lost some of this, and this question has made me realize that. Quite depressing.)