Security Capital Assurance (SCA) is to gain the assistance in a deal which would see the bank agreeing to cancel lawsuits and $3.5 billion in credit defaults in return for a cash payment of $500 million.
XL, a reinsurer based in Bermuda, will pay a further $1.78 billion in cash to the bond insurer.
A total of eight million shares will also be issued to Security Capital from XL, which in turn is selling around $2.5 billion of assets to fund the deal.
New York State insurance superintendent Eric Dinallo, who helped to broker the deal, told Reuters that the bond insurer would benefit hugely from the agreement.
"SCA is going from essentially on the brink of insolvency to a surplus of about $1 billion," he commented.
"It gives us some light at the end of the tunnel that even an extremely distressed bond insurer ... can be brought out of a pretty dire situation."
Formerly, SCA operated as a subsidiary of XL.