This issue goes beyond health insurance. It is about insuring the future income of a player and his value as an asset to the team should a long-term injury occur. In the same way a private owner lends art to a museum and asks it to pay an insurance premium to display a painting, the N.H.L. and its team owners are asking the I.O.C. to pay the insurance premiums on the assets they are lending out for the international showcase.

It is not an abstract problem. At the 2014 Sochi Games, the Islanders’ John Tavares tore a knee ligament while playing for Canada and missed the rest of the N.H.L. season.

With the I.O.C. no longer willing to cover those premiums and the International Ice Hockey Federation unable to cover the cost by itself, the governing bodies are reaching out to all parties involved to find a resolution.

“The I.I.H.F. has asked the national associations and the national Olympic committees if they are willing to cover that, but from our perspective, that responsibility rests on who is organizing the event and who is collecting all the revenues from the event,” Nurminen said. “In our opinion, the same party should pay the bills, and that’s not us. All the countries replied to the I.I.H.F. that they are not willing to pay for the insurance or the travel or any of the other expenses that are related to having the N.H.L. players participate in Pyeongchang.”

At least 150 N.H.L. players are expected to be selected for their countries’ Olympic teams, requiring the league to shut down for the duration of the Games. European leagues plan to make their players available, but none will have to shut down for three weeks, as the N.H.L. will.