If something has been abandoned, you can call it derelict. Even if a person has abandoned his responsibilities, you can say that he is derelict in his duties. But don't call a lost child derelict — unless, of course, he has neglected his chores.
As an adjective, derelict describes something that is rundown, neglected, or in deplorable condition, but the word can also mean "negligent in duty." The politician was so busy using his office for personal gain that he was derelict in his duty to the people who voted for him; he hadn't been present at a vote in months. As a noun, a derelict means a homeless person.