An AI system can theoretically "become an independent economic agent" in a practical sense without legally owning money. For example, suppose it has access to a lot of resources owned by some company, and nobody can understand its logic or its decisions; and blindly letting it handle those resources is the only way for the company to stay competitive.
IKEA is an interesting case: it was bequeathed entirely to a nonprofit foundation with a very loose mission and no owner(?)
https://www.investopedia.com/articles/investing/012216/how-ikea-makes-money.asp
Not a silly question IMO. I thought about Satoshi Nakamoto's bitcoin - but if they're dead, then it's owned by their heirs, or failing that by the government of whatever jurisdiction they were in. In places like Britain I think a combination of "bona vacantia" (unclaimed estates go to the government) and "treasure trove" (old treasure also) cover the edge cases. And if all else fails there's "finders keepers".
Fascinating: