Is it permissible to pay Zakat to a indebted relative who claims to have been robbed, while people accuse him of squandering money on unlawful things?

The basic principle is that the mudarib (managing partner) is trustworthy and is to be believed under oath when claiming that money was lost or stolen or that the business incurred losses, unless there is evidence or indications of his negligence or betrayal. So, if the money was stolen from your cousin, he is not liable for it. If the capital providers insist on taking it from him, they are unjust. If he is compelled to pay the money out of fear of harm, then it is permissible to give him from zakat because he is an gharim (one in debt). However, if his betrayal and squandering of the money are proven, then he is disobedient and must guarantee the money, and it is not permissible to give him zakat until after his repentance.