。
Apparently they played dead and escaped the danger.
Literal
Dead pretend do-[and-て] difficulty [obj-を] escaped hearsay.
死んだフリ (フリ often in katakana, 'pretend/act') is the noun phrase 'pretending to be dead.' It's a fixed collocation paired with する: '[...の]フリをする' = 'to pretend [to be X] / to act [like X].' Here 死んだ modifies フリ attributively. 難をのがれる ('to escape danger/disaster') is a set expression; 難 means 'difficulty, disaster,' and のがれる ('to escape, to evade'). The final ~そうです is hearsay — 'I hear that / apparently.'