Adverbial "home" works like other little words in English that follow a word for a motion and indicate the destination of that motion. There is no standard term in common use for these words, but it would be reasonable to call them destination particles.* Here are some examples:
Be sure to take the trash out tonight.
Next, we should carry the couch up.
Come inside before it gets dark.
Thompson's pass inside never found its target.
The King called back the courtiers whom previously he had sent away.
Notice, as in the case of "inside", that these can often serve as an adjective as well as an adverb (modifying the noun "pass" above).
Now here are some well known sentences and phrases to memorize, all containing "home" as a destination. Most other usages of "home" as a destination particle work by analogy with these. I've marked both "home" and the word or phrase that it modifies in bold:
Come home before it gets dark.
And this little piggy cried "wee wee wee" all the way home.
The trip home always seems shorter than the trip there.
Do you know the way home?
The show was good, but it was nothing to write home about.
We're almost home.
The example from This Little Piggy is instructive.† "Cried" doesn't indicate motion. The motion in that sentence is provided by the phrase all the way, which functions as an adverb indicating that the piggy cried while going somewhere. The word home here works in the usual manner of destination particles: it follows the word or phrase for the thing whose destination it supplies. It indicates that "all the way" terminates at "home".
"Home" as the object of a verb
If "home" doesn't follow a word or phrase for some sort of motion, or at least something that has a destination (e.g. "The road home is full of potholes"), then "home" won't be heard as a destination particle. So, if you say:
I study home.
a listener will understand "home" as the object of "study", so the sentence means that you study some place or object that you call "home". There is no ambiguity regarding whether "home" functions as an object or a modifier, in this sentence or in any of the other examples.
Now you're ready to understand what happens in this sentence:
I read letters home.
A listener will understand "home" as the destination of the letters, not as the location where you read the letters. If the notion of destination can somehow make sense with whatever preceded "home", then "home" can comprehensibly play the role of destination particle. But there can be no rule precisely demarcating how far you can push the analogy with the very well known examples above and with other destination particles. The following sentence goes too far and will be heard as ungrammatical:
The bomb squad inspected packages home.
Adverbial "home" as location, not destination
Here is something else that a rule likely can't fully characterize. There are a few contexts where adverbial "home" indicates a location but not a destination, analogous with here and there in these same contexts:
This little piggy stayed home.
Are you home?
We'll be home when you arrive.
I don't want to sit home all day.
This doesn't generalize. If you memorize the above sentences, you'll know pretty well when this sense of "home" works in English. It is possible to use "home" in this way with other verbs, but that will usually be heard as creative or unconventional language. Even "sit home" is somewhat unusual.
* There is specialized terminology for these words, in use by linguists, mentioned here, but that terminology clashes so strongly with the terminology in common use that I think it introduces more confusion than it prevents.
† Everyone who learns English must memorize This Little Piggy. Its five short lines teach a great deal and are a widely recognized cultural landmark.