Is it permissible to give zakat to a neighbor who has children who do not support him, and a divorced daughter living with him with her children, and he lost money in a failed project, and he is now working transporting children to cover his expenses?

If the man mentioned does not find that his profession suffices to meet his essential needs, and his wealthy children do not spend on him, then he is considered poor and eligible for zakat (definition). However, if his profession suffices to meet his essential needs and the needs of those he supports, then he is not considered eligible for zakat, and what is given to him is considered an act of charity (sadaqah (definition)). If his work does not fulfill his needs and the needs of those he supports, then he is considered a recipient of zakat, and similarly his divorced daughter if he is unable to spend on her.