The government decided in 2012 it would keep any future profits on the stocks because of the risk taxpayers took in rescuing the agencies for $187.5 billion, a sum that is just now in the final stages of being repaid.
That decision to "sweep" profits to the U.S. Treasury essentially wiped out all shareholders, including those with the "preferred" status they theoretically have. Perry, Fairholme and others argue that the "sweep" decision is unconstitutional.
To earn the big payout the funds are targeting, two things likely need to happen: First, the courts need to overturn the sweep decision, which would allow Fannie and Freddie to begin accumulating profits instead of passing it on to the Treasury. Second, Congress needs to reform Fannie and Freddie without liquidating them, thereby allowing shareholders to start collecting the profits on their business.
If both things happen, that would mean big money for the investors—preferred shares of Fannie and Freddie are worth a face value of $33 billion today. But the same shares will likely be worthless if the funds lose in court and the new Senate liquidation legislation proposed this week passes.
(Read more: After Fannie and Freddie—Who's next?)
The recent congressional proposal does not address the investor issue and GOP Sens. Bob Corker of Tennessee and Mike Crapo of Idaho have said the courts should decide if the hedge and mutual funds are paid.
(Read more: Corker: Deal to end Fannie, Freddie is just right)
Separately, hedge funds that trade so-called "agency" mortgage-backed securities—packages of home loans made by the government-affiliated agencies like Fannie and Freddie—aren't concerned about their market going away.
"Even though the plan relies on private capital to take the first 10 percent of risk, I believe that the government will always step in as the mortgage lender of last resort, as it has been for the past six years," said Reza Ali, founder of $1.5 billion bond-focused hedge fund Prosiris Capital Management. "I do not believe politicians will permanently abandon the housing market when the next crisis hits and drives private capital away."
Another longtime government-backed mortgage investor said the Senate plan to attract private capital to the market would provide fresh trading opportunities.
"It actually creates a ton of volatility and uncertainty around the market, which for me as an investor is something that I think is enticing and I'm excited about," said Troy Dixon, a former senior mortgage trader at Deutsche Bank who is preparing the launch of a potentially $200 million hedge fund this summer, Hollis Park Partners.
"From my perspective I know you cannot shrink that market to zero so it's not like the market's going away, i.e. a non-agency market," Dixon added. "It's just too big a portion of our economy and the American dream to go away."