That person has it now. They mjght volountarily be willing to send it back with another transactions or the courts could force them to do so (as in give fines, request keys, send to prison, or just have the government own and ooerate all the wallet keys and simulate transactions eith blockchain just as the technology used in a very janky way)

What happens if the owner dies? How is the NFT transferred then?

Similarily, either the government does all the transactions with 'your' keys for you, or you write down the keys in your will and have someone of trust (e.g. a lawyer) do the partitioning/transactions part in your stead.

Who checks that the original NFT was issued correctly?

The seller and buyer beforehand, mostly

What about properties that are split? What happens if the split isn't represented in the NFT correctly (e.g. due to an error)?

Rebalance by having everone affected send their portions for redistribution to a trusted entity

As you've said yourself, NFTs seem wholly unsuited for keeping track of general ownership on a large scale. All the problems do have solutions, but they're either complicated for the owners or it's someone else controlling people's keys, defeating the entire point.