It’s a good question, and obviously it depends on the different circumstances of each godol.
Rav Chaim Kanievsky’s daughter, Rebbetzin Kolodetzky, has taken over domestic duties in their house.
When the Gateshead Rosh Yeshiva, Rav Leib Gurwicz’s first wife was nifter, a bochur slept in the house with the Rosh Yeshiva. I’m not sure if he had any other duties.