"path to safety" is a correct and usable phrase in written English.
It can be used to indicate a physical or metaphorical way or route towards a safe or secure place or outcome. Example: "The storm was approaching quickly, but the hikers were relieved to see a clear path to safety through the dense forest."
"In the world we have entered, the only path to safety is the path of action.
In the world after September the 11th, the path to safety is the path of action.
With the lights off, you're forced to navigate your path to safety by sound cues alone.
It is helping refugees and their families along their precarious path to safety.
In a fantastical country where the power of story is paramount, Mosca and her goose weave a path to safety.
Britain and Denmark, among other allies, had already offered their own Iraqi workers a path to safety.
The research results fulfill user needs not satisfied in existing crane cabins and suggest certain changes to existing standards on the path to improved safety.
Officials were taking no chances this year, and on Monday the president, Benigno Aquino III, appealed for people in Bopha's path to move to safety and take storm warnings seriously.
He spoke of the "beth path forward to safety and security"; he asserted that Syria's regime uses chemical weapons "to the very day"; he argued that the Soviet Union collapsed "because of America's leadership and America resolve".
Until people and places change, city bike-sharing programs may be a critical step on the path to improved bicycle safety.
The mayor is connecting the McCormick Place upgrade to a planned $278 million facelift for Navy Pier that will include a new interactive fountain at its entrance, an expanded Children's Museum, more bars and restaurants and the building of a $48 million "flyover" bike path to ensure guests' safety while walking to the pier, NBC Chicago reports.
