The phrase "have little to lose" is correct and usable in written English. Generally, it is used to convey the idea that someone already has very little and stands to lose very little should something go wrong. For example, "With worsening economic conditions, people in the neighborhood have little to lose, so they are more willing to take risks.".
But Liberia may have little to lose from sanctions.
Most discharged workers do file, because they have little to lose by doing so.
The British, he said, would have little to lose by not joining.
Perhaps the Tories reckon that, facing humiliation at the polls, they have little to lose.
And, with high unemployment, millions of urban poor, particularly in the capital, have little to lose.
The Blazers are definitely more worried about this because the Grizzlies have little to lose.
There is an important corollary: women have little to lose by ruffling feathers.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union