The complaint was filed in the U.S. District Court in Manhattan by the liquidator of Luxembourg-based SLS Capital SA, which failed in 2009, the same year Elias died.
According to the complaint, HSBC had been a custodian of life insurance policies used as collateral for bonds that SLS sold to investors, and which were falsely marketed as safe.
An HSBC spokeswoman declined to comment.
Companies in the so-called life settlement business buy life insurance policies on older individuals, and can collect death benefits when the insureds die. Securities backed by such policies are sometimes known as "death bonds."
One prominent seller of these bonds was Keydata Investment Services, which had business dealings with SLS, and whose sale of the bonds caused big losses for thousands of UK pensioners.
Keydata also failed in 2009. Britain's Serious Fraud Office dropped a probe into that company in May 2011, saying it lacked enough evidence to prosecute.
According to Friday's lawsuit, SLS began selling bonds in 2005, with investors buying them directly from the company, or buying bonds issued by Keydata and securitized by SLS.
When SLS ran into cash-flow problems, Elias began siphoning investors' collateral to fund other risky ventures and support his lavish lifestyle of "corporate jets, luxury yachts, and island resorts," the lawsuit said.
HSBC, for its part, ignored multiple signs of suspicious activity, including that Keydata looked "like a Ponzi scheme" and had ties to Elias, and "turned a blind eye" when Elias sold much of the collateral in a 2008 "fire sale," the lawsuit said.
"Simple justice demands that HSBC be called to account for its role in (Elias') fraud," the lawsuit said.
Born in Singapore, Elias's business interests stretched from operating a Malaysian club that leased jets and yachts to the ultra-rich who could pay $1 million a year for membership, to the ownership of 800,000 acres in the Brazilian rainforest.
According to SLS liquidator Yann Baden, the lawsuit belongs in New York because HSBC Bank USA operates there, and much of its alleged improper conduct occurred there.
The case is SLS Capital SA et al v HSBC Bank USA NA, U.S. District Court, Southern District of New York, No. 14-06846.
(Reporting by Jonathan Stempel in New York; Editing by Leslie Adler)
By Jonathan Stempel