Is a sister held accountable, in Islamic law, if she does not inform her brother-in-law that her sister bought gold with his money without his knowledge, and she does not possess the money to return it? And what should she do?

A wife is not permitted to dispose of her husband's money without his permission, unless he withholds her maintenance and the maintenance of their child, in which case she may take what is sufficient for her needs. Your sister has acted wrongly by her actions, and she must repent and return the money to her husband, even if indirectly. You must advise her by instilling in her the fear of Allah so that she returns the money. If she does not, then threaten her with informing her husband, and if she still does not desist, then inform him to save his money, unless doing so would lead to a greater harm.