Property sharing of a childless muslim woman

The fact that her flat was purchased with the sale proceeds earned out of the flat owned and thus sold by the husband does not change anything. There's no distinction between someone's self-acquired property and ancestral property in Muslim law. If the person dies interstate (i.e. without leaving a will,) the rules of inheritance will more or less be the same.

Assuming the widow is Sunni Muslim, and assuming that her parents are deceased, her property will be divided equally among her three brothers (as the residuaries.) If her parents are alive, they will inherit primarily as sharers. Her father gets 1/6th, and mother gets 1/6th (and not 1/3rd since the deceased has more than 1 brother,) and the remaining share out of that will be inherited by deceased's 3 brothers equally as residuaries.

Assuming that the childless widow is a sunni muslim  the rights of her heirs are as follows:   The  deceased childless Mulim woman's  3 full brothers  would get preferential  equal rights over her flat property   and not her mother in law and her 3 sons as her full brothers are residuaries in their own  right in the absence of her parents and belong to 2nd subclass of class1 legal heirs   under Muslim law and MIL and BILS are very distant kindred..the flat property will have  to be divided into  1/3rd portion  each among   widow's 3  brothers. or equally shared among the  three.or disposed of and the sale proceeds  will have to be divided in to 1./3 rd part each among her  3 brothers.

Assuming that the childless widow is a sunni Muslim  the  deceased childless Mulim woman's  3 full brothers  would get preferential  equal rights over her flat property as they  belong to 2nd sub class of class 1 legal heirs and residuaries in their own right in the absence of her parents and not her mother in law and her 3 sons as  they come under distant kindred category..The flat property will have  to be divided into  1/3rd portion  each among   widow's 3  brothers   or shared equally by them or disposed off and the sale proceeds should  be divided 1nto 1/3rd  part each among the 3 brothers.