Yes, venues are being asked for refunds, and some may restructure loans

Sports fans awaiting refunds wonder if they're being played, Crain's New York Business reported two days ago, describing baseball having trouble getting refunds from teams desperate to maintain some liquidity amid the coronavirus crisis.

From the article:

Some squeezed owners and arena operators are preparing to ask bankers for waivers to their loan covenants.
“We’re starting to have those conversations,” Fitch Ratings analyst Chad Lewis said.

I don't think the Barclays Center can get a waiver regarding mandatory payments in lieu of taxes (PILOTs) required to pay off arena construction. The arena does have a reserve fund, and the owner of the Brooklyn Nets and arena operating company is a billionaire.

But the outlook has to be concerning. And while Barclays has announced cancellations and postponements, it does not necessarily control the process. Which means, oddly enough, that a concert scheduled for June 20 is proceeding, at least according to the arena's web site. [Update 5/21/20: it's been postponed.]