Many fashion houses literally burn their unsold products to create this scarcity or create limited runs. DeBeers have a heavy control over the diamond industry. If an artist says they'll only create unique pieces (a 1/1 collection) then while they could create more in future, they'll still have a market determined value.
The market dictates the value. As a test, create and mint an exact replica of a Bored Ape NFT and try to sell it for the current minimum price of 32 ETH or around $150k.
The marketplaces verify the collections. So if you're buying from a famous artist on OpenSea, you know the NFT is the one from that artist. There are copycat collections but it's no different from someone trying to flog a fake Banksy a the local shopping mall.