I am pretty ignorant of what entity owned the entire World Trade Center complex before they were attacked. What, if any, insurance policy did they have for the buildings?
Perhaps the idea of them being destroyed was such a farfetched idea that nothing similar to a small business insurance plan was even proposed or considered, but condominiums on the Gulf of Mexico near where I live must have insurance policies or else they're up to face massive losses whenever a significant hurricane hits. Obviously there was a massive loss in property assets taken on that day.
Were any owners of the original complex able to claim anything at all after the attacks?
As soon as the day after the attacks,^1 the New York Times reported on the "dozens of insurers" that would be sorting out the damages. It said the effort would take years, and sure enough, it did.
The primary representative of the consortium that owned the WTC complex was real estate mogul Larry Silverstein. He signed a 99-year lease on July 24, 2001. Like most new owners of real estate, he also signed an insurance policy right around the same time. When the towers fell a couple of months later, that insurance policy became the focus of a years-long legal proceeding.
Most homeowners' policies don't cover terrorism, but it's not uncommon in commercial policies. (Actually, the Terrorism Risk Insurance Act of 2002 makes it hard to avoid terrorism coverage in most policies today.) The WTC policy in particular would obviously have terrorism coverage, given that the 1993 bombing had a major insurance impact. So when Silverstein went to collect for 9/11, the only question was: was the loss technically one "qualifying event," or two? Ultimately, the insurance payout was $4.6 billion - which took until 2007 to sort out.
But that wasn't the end of it. Silverstein sued the insurers again in 2008, won $1.2B in 2010 from American Airlines and United...on and on we go. Finally, in 2018, the last lawsuit was settled - against Silverstein. None of this is personally enriching him, though - all of these awards have gone into the rebuilding of the WTC complex, including the famous "Freedom Tower" (the new 1 WTC).
The whole thing is all quite messy. You can find scholarly articles about the 9/11 insurance situation in Tort and Insurance Law Journal, the Journal of Risk and Insurance, etc. It has permanently transformed the way commercial insurance policies work.
^1 - This Snopes article cites an insurance-related story by Reuters from September 11 itself, but the only version of that story I can find online is a Fox News repost from 2015, so I went with the NYT 9/12 source.
Edit: Some additional reading I did not include last night: One Hundred Minutes of Terror That Changed the Insurance Industry Forever from the Insurance Information Institute.