'secure their safety' is a correct and usable phrase in written English.
You can use this phrase when you are referring to a group of people whose safety you want to take measures to guarantee. For example, "The government must take immediate steps to secure their safety and protect them from any potential danger."
As the next 3 billion or so of the planet's people come online, it's never been more important to secure their safety, their privacy and the security of their personal data.
They climb aboard to scattered cheers, secure their safety belts, check the instruments yet again.
"It's difficult to secure their safety, and their trip will have a negative impact on bilateral relations," the Foreign Ministry said in a statement.
A Turkish official told the AFP news agency that the two pilots were alive and that Turkey was seeking to secure their safety.
Your article says that in Japan "travelers shouldn't expect any help from the government to secure their safety or get out of trouble".
It means a Yorkshire draw with full bonus points (which they will achieve with three more wickets in the huge amount of time remaining) will secure their safety, because Kent cannot realistically beat Durham.
Cheltenham were also relegated to the Conference for the first time since 1999, as Hartlepool secured their safety.
And, having looked doomed in the winter break, they secured their safety with two games to spare, eventually finishing a very respectable 12th.
However, Rovers will take considerable consolation from the role he played in helping them avoid relegation in their first season in the Super League in the 14 appearances he made last year, including a 42-6 win at Hull in September which secured their safety.
Elche, whose point has secured their safety from relegation, failed to test Barcelona keeper Jose Manuel Pinto in the 90 minutes.
Lincoln, who would have secured their safety from relegation with victory, are now eight points clear of 21st-placed Hayes & Yeading, who have three games remaining.
