What is the correct action to take regarding the remaining money that was collected to help a sick man who later passed away, given his wife's refusal to receive it and his brother's pledge to care for the family, and is it permissible to designate this money for the benefit of righteous people?

You are an agent for the donors. As long as you were instructed to disburse the funds to a specific person and that person refused them, you must inform the donors of this. So, whoever wishes for their share to be an ongoing charity (sadaqa jariya), or a specific charity, then do so. And whoever wishes for their money back, return it to them, because a donation is not complete until it is taken possession of. If, after making an effort, you are unable to identify the donors, then give their money as charity in good causes and for the benefit of Muslims, and it is preferable for it to be an ongoing charity. If among these funds there is zakat, it is not permissible to disburse it except to its rightful recipients mentioned in Surah At-Tawbah, verse 60.