What is the ruling regarding doing family Quran khatam when someone passes away?

So there are three aspects to this question. Number one, is it permissible to recite Qur'an with the reward going to the deceased? So in the Hanafi and Hanbali Madhab, yes, it is permissible because the Qur'an is considered a form of sadaqah. And we know from the hadith in Sahih Muslim that sadaqah, it benefits the deceased. Other famous scholars such as Ibn al-Qayyim, Ibn Taymiyyah, they also held this view. Now, the second part is, is it permissible to gather together to recite Qur'an? Yes, that's permissible, just as you would, for example, gather together in a mosque to give sadaqah. No issue with that. The problem aspect comes when you specify a certain day that it must, for example, be done on day 40. This is where it becomes problematic because there's no authentic hadith. As we mentioned a hadith previously, there's no authentic hadith to say it must be done on day 40 or this is what you have to do. So if you're specifying a day like that, saying it has to be done on that day, then no, that should be avoided. But generally speaking, reciting with the intention of it benefiting the deceased that's permissible.