Is zakat obligatory for those who are poor, addicted to drugs, close relatives, and able to work?

Those most deserving of zakat are the religious people who adhere to the Sharia. If it is thought that disobedient relatives will spend it on acts of disobedience, then it should not be given to them. Otherwise, there is no impediment. They must be advised and warned of Allah's punishment if they do not repent.