Time is running out for family members of the people who vanished aboard missing Malaysia Airlines Flight 370.

The deadline under international law for next of kin to make a claim against the airline is Tuesday, the two-year anniversary of the passenger jet's disappearance.

Dozens of relatives of the 239 passengers and crew members who were on the flight have already collected compensation, according to Malaysia Airlines. But others have been struggling with the legal and emotional complexities surrounding the mysterious loss of the plane. And some are accusing the company of trying to dodge responsibility.

Voice370, a support group for families of people lost on MH370, claims the recent restructuring of Malaysia Airlines into a new corporate entity appears to be a "ploy to shield itself from liability of negligence or other claims, which may not be covered by their liability insurance."

After MH370 disappeared, and another plane operated by the airline, MH17, was downed over Ukraine months later, the already struggling carrier was pulled from the stock market and taken private by Malaysia's sovereign wealth fund.

Backed by a new law passed by the Malaysian government, the fund appointed an administrator last year to oversee the transfer of assets and liabilities.

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The relatives' group says it fears the moving of assets into the new company is likely to leave nothing for them to pursue through legal action.

In a statement, the airline's administrator, Mohammad Faiz Azmi, didn't comment directly on the group's claim about the asset transfer. But he did say the company has sufficient insurance coverage to meet its obligations to compensate family members under international law.

Malaysia Airlines "remains committed to continue engaging the [next of kin] in good faith with regard to ensuring a fair and equitable compensation," Azmi said.

Andrew Yong, a litigation lawyer in Malaysia who's not involved in the cases, said it's the airline's insurer that's most likely to handle the families' legal claims.

"The idea that any of these claims would be paid out out of the assets of Malaysia Airlines is quite unlikely," he said.

A total of 42 next of kin have collected "full compensation," said Azmi, although he didn't disclose the amount.

As of last week, Azmi said he had approved 96 requests from relatives to begin legal proceedings and rejected none. But the fact that the lawsuits require his say-so to go ahead has further angered some family members.

"As long as the administrator's giving permission for these lawsuits to be filed, I think there shouldn't be too much concern," said Yong, the litigation lawyer. But he said if the administrator were to be found to have been blocking any claims so that they miss the deadline, that could give grounds for fresh legal action.

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Ye Lun, a Chinese man whose brother-in-law was aboard MH370, told CNN his family was refusing to take a compensation deal with the company because it requires them to sign a document granting the airline impunity — something they're not willing to do.

"We simply want our man back," he said.

Family members' suffering has been deepened in the case of MH370 by the continuing uncertainty over what exactly happened to the aircraft after it dropped off radar. Investigators believe it went down in the southern Indian Ocean, thousands of miles from Beijing, its intended destination.

The main wreckage of the Boeing 777 and the remains of those on board has never been found and investigators have been unable to determine why it flew wildly off course. A wing part found washed up on an Indian Ocean island last year was confirmed to be from the missing jet, and authorities are now investigating whether a piece of debris discovered on the coast of Mozambique at the weekend is also connected.

Lawyers have said that without closure, families have found it emotionally difficult to move forward with compensation claims.

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Some are turning to the U.S. court system.

In January, the sons of Philip Wood, an American citizen who was on the plane, filed a lawsuit against Malaysia Airlines in federal court seeking damages.

Steven Marks, the lawyer acting on their behalf, said at the time that the compensation offer from the airline's insurer was far from satisfactory.

Seeking a judgment in the U.S. system "could mean a compensation package of many, many millions of dollars," he told CNN.

Marks said in January that he planned to file lawsuits for some non-U.S. families whose loved ones bought their tickets for Flight 370 through American travel websites like Orbitz.

Steve Wang, a Chinese man whose mother was on the plane, said Thursday he was working with a lawyer to begin legal action soon.

For him and others, the clock is running down as Tuesday's deadline approaches.

-- Bex Wright, Yuli Yang and Rene Marsh contributed to this report.