According to the Shari’ah, the question’s mentally unstable brother also has a right to a portion of his parents’ legacy, which will be given to any other inheritor who will use it to spend on his necessities. Since in the mentioned situation the biggest brother has been taking responsibility for him, he (the biggest brother) will be given his (the mentally unstable brother’s) portion of the inheritance and, with honesty, he will spend on the necessities of his mentally unstable brother.
And Allah knows best.
کمافی بدائع الصنائع في ترتيب الشرائع: (أما) حكم المال فأما المجنون فإنه يمنع عنه ماله مادام مجنونا، وكذلك الصبي الذي لا يعقل؛ لأن وضع المال في يد من لا عقل له إتلاف المال. (7/ 170)۔