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Question: If someone owns a nursing home that serves chametz on Pesach to the residents, would selling his chametz before yom tov take care of all the halachic issues?
Answer: In addition to the other prohibitions of chametz on Pesach, there is another prohibition known as “rotzeh b’kiyumo”(wanting something to exist), ie. benefiting by having the chametz around.
To illustrate this, the Shulchan Aruch (409:7) rules that one cannot rent a pot to a non-Jew if he knows the renter will use it to cook chametz on Pesach. The reason for this is because if the pot would be on the fire with nothing inside of it, it would become ruined; therefore, the owner wants the chametz to be inside the pot. Since he is benefitting through the existence of the chametz, it is considered a forbidden gain derived from chametz on Pesach.
If a person owns a nursing home, he has to serve food to the residents in order for his business to stay open. Even if he sells his chametz, he still wants it to exist so that he can make profits off his nursing home. It would seem that the only solution would be to find a way not to take profits from the nursing home for the duration of Pesach. Rav Elyashiv actually points out that if one wants to avoid any problems, he should not profit from a business that deals in chametz on Pesach at all. He would have to sell the business in a way that precludes him from taking such profits, and he should speak to a Rav to discuss how to do this properly.