It depends on the terms of the building. There was an Ask Metafilter question recently from some people who bought a house, intending to live there for years, and had some very nice landscaping done. A few months later, they learned the husband's job was being transferred and they had to sell the house. They got much more than what they paid for it because the landscaper's work had increased the value, and he was coming after them for a share of the profits and they wanted to know what their rights were. The answers they got were overwhelmingly that they were in the clear. They paid the landscaper for his work, it was work for hire, and it was done.
Similarly, my grandfather (since Harry brought him up) has a house which is on a valuable property. The house itself has fallen into disrepair. It would need to be torn down and rebuilt to be habitable again when he passes. So his heirs have the choice to pay whatever it would cost to refurbish the house or tear it down or rebuild it, or they can just sell it as is and let whomever buys the land deal with it, which is likely to happen. A hundred years from now, let's say the new owners of the house turn it into a hotel and make pots of money. Should we be entitled to a share? Of course not.
Or, to turn it back to culture for a moment, let's say that my cousin, who is a musician of some local acclaim, becomes super-famous in the next few years and a hundred years from now, they want to turn Grandpa's house into a museum about his work. Who should get the profit from it? Well, I think it depends. The owners, whomever they might be, own the house, absolutely. But let's say my children have inherited, as part of my personal belongings, rare photographs of him and the house wants to exhibit them. Then my children should get paid a license fee for it.
Look, if something is in the public domain, it doesn't mean theoretical heirs can't profit from it too. Bram Stoker's great-grandson published a mediocre Dracula spin-off a few years ago that likely would not have seen the light of day had he not cashed in on the Stoker name. The public domain just means that *I* could write one too, because the work has passed into the public domain and become part of humanity's shared cultural heritage. If JK Rowling's great-grandchildren want to write their own Harry Potter novels, who is stopping them?
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