Is it permissible for someone who found a sum of money and a gold piece, and is in dire need of them after being expelled from his job, to dispose of them to the extent of his need and necessity, knowing that he tried to contact the number found with the money repeatedly without success?

It is impermissible to dispose of a lost item (Luqatah) except after publicizing it for a full year in places where people gather. Disposing of it before that is a violation of Islamic law and a betrayal of trust. The one who does so is sinful and is held liable for it. Necessity does not justify such an action.