I think you mean can you get rid of this person's things without inviting trouble. You are in lawful possession of the items, and I think you have a moral obligation to keep them safe if you can, but unless you were paid or given some other compensation for keeping the items, I don't think you would be likely to be prosecuted if you were to get rid of the items.
Why don't you begin by asking this person? You've sent him letters, but are you sure he's still in the same jail? I think the fact you haven't gotten a response might be because he hasn't gotten the letters, your first step should be to verify your sending the letters the right place.
Legally, you probably would not be prosecuted for discarding the items, especially if the value of them was not that high. However, morally, you should make a good faith effort to find out what facility he is and try to return it to him, his attorney, the jail or a family member. Why invite trouble!?