A New York art gallery is in a $1.35 million legal dispute with South Korea's Gwangju Biennale Foundation, a case that demonstrates the potential pitfalls of international loans as more fairs and exhibitions spring up around the world.

An onyx sculpture lent by Michael Werner Gallery to South Korea's Gwangju Biennale Foundation Michael Werner Gallery, New York

At issue are three onyx sculptures by the late American artist James Lee Byars ; the works were lent by Michael Werner Gallery for the 2010 biennial and were damaged during removal after the show and in transit back from South Korea, according to court documents submitted by the gallery.

The gallery, the biennial and the biennial's insurance company have been fighting the case in a South Korean court since 2011. A judge could rule on the case as early as Friday, according to gallery officials.

Mr. Byars was a performance artist and sculptor who blended minimal and conceptual art. He died in 1997.

The three works are slender blocks of pistachio-colored onyx between 4 and 6 feet high, with their raw, reddish surface left intact and letters carved on one side to represent the eyes of the figures. Each was valued at $450,000.

The sculpture was damaged in transit back to Germany. Michael Werner Gallery, New York

The Gwangju Biennale is one of Asia's most prominent contemporary-art biennials. It borrowed the three works for its 2010 show, which was curated by Massimiliano Gioni, associate director of New York's New Museum, who went on to helm the prestigious Venice Biennale in 2013.

"Unfortunately, risks are inherent in any loan, and it is devastating and embarrassing when anything like this happens," said Mr. Gioni, whose contract with the Gwangju Biennale ended a few weeks after the show closed.

Michael Werner Gallery, which has galleries in Germany, London and New York, signed a borrowing agreement stipulating—crucially, it turned out—that the biennial would insure the work through a South Korean insurance company.

In hindsight, gallery officials said, that was a mistake.

Instead, they said, they should have stipulated that the borrower pay for the gallery's regular insurance company to insure the works for the trip to South Korea. That is a common practice, and while it can be more expensive for the borrower, it allows the lender to negotiate any damage claims with an insurer with which it already has a relationship, art experts said.

One of the three Byars works was damaged after the show during deinstallation, according to both sides. All three were damaged in transit back to Germany, where they had been in storage, according to court documents submitted by the gallery. Photographs reviewed by The Wall Street Journal show cracks and chips in the onyx, as well as damage to the crates the sculptures had been packed in.

The gallery claimed total loss, arguing that inherent to Mr. Byars' works was the integrity of the pieces of onyx he had chosen.

"I'm devastated because those are seminal works," said Gwendolyn Dunaway, Mr. Byars' widow. "They were the first works where my husband started using text as eyes on figures."

The biennial, in an email to The Wall Street Journal, pointed to a condition report made before the loan, showing the onyx already had flaking or loss in some spots, which the gallery said was natural because of the raw state of the gemstone's surface.

The biennial argued that if the damage during deinstallation constituted totaling the sculptures, then the works had already been totaled before they arrived. Both sides agree damage included the breaking-off of a 2-inch piece.

The biennial's insurer, Dongbu Insurance Co., didn't respond to requests for comment.

In the increasingly global world of contemporary art, works zigzag around the world. Sometimes art is damaged. Most disputes are resolved in mediation.

Instead, the gallery found itself navigating the South Korean legal system.

"It keeps taking the weirdest twists and turns," said the gallery's New York director, Justine Birbil, who filed an affidavit challenging the biennial's argument that damage was inevitable because of the nature of the material. The works had been moved before without damage, she said.

"In this case, they've categorically refused" to negotiate a settlement, gallery partner Gordon VeneKlasen said of the biennial and its insurer.

In an email, biennial spokesman Jisu Cook said the foundation was concerned other galleries may be reluctant to lend works to the biennial because of the lawsuit. He said the foundation had promptly informed the gallery of the damage.

"The issue is how one defines the extent of the damage—whether it is a total loss or partial damage," Mr. Cook said.

Mr. Gioni said lenders and borrowers should take every precaution to insure and protect artworks. He added he hoped the case wouldn't discourage lenders from participating in biennials worldwide.

"As art becomes a more precious commodity, it is more important that we allow for ideas and art works to circulate: If they simply end up in storage and bank deposits, it would be a huge loss for the education and the spiritual growth of thousands of people," he said.

Write to Jennifer Maloney at jennifer.maloney@wsj.com