From my understanding the business (in this case your vet clinic) is owned by the household, which is why it shows up up in the retail panel on every sim in the house. So, when one person in the house dies, even if it's the person who started the business, it should still belong to the rest of the family. Based on your initial post, I'm assuming the answer is yes, but did the daughter live in the same household as her dad? Or did she move out at any point before he died, which would remove her as one of the owners?