Question: Will invitation of the deceased to stay at home to partake of food offerings distract the person from Nianfo (practice of mindfulness of the name of Amitabha Buddha – ‘Amituofo’)?
Answer: There is no Buddhist practice to invite the deceased to stay at home because it is not advised to do so. What we should do is urge sincere Nianfo to reach Amituofo’s Pure Land as swiftly as possible, once dying and as continually as possible after death up to 49 days, which is how long the average deceased’s consciousness might be around before rebirth. Details on how to do so are taught in the ‘Destination Pureland’ course: http://thedailyenlightenment.com/2016/04/destination-pureland-how-to-have-the-best-rebirth-5th-run
Food offerings can be put up at home in case the deceased is around, but we should not purposely invite anyone to come to stay and partake of them. If around, the food can be consumed in essence, and the person be guided by the following practice. Even if not around to be guided, these practices listed at https://purelanders.com/2016/07/19/what-should-be-chanted-during-after-a-funeral will still create merits that can alleviate suffering and facilitate a good rebirth. The longer the deceased stays, the more likely will attachment be, while the law of karma will still force rebirth to elsewhere eventually and accordingly, with much suffering due to much attachment.