save (one's) skin
To rescue one from failure, danger, or disaster; to prevent something bad from happening to someone. Thanks for bringing me some extra cash—you really saved my skin, there! The company is in dire need of new investors to save their skin.
save someone's skin
and save someone's neck; save one's baconFig. to save someone from injury, embarrassment, or punishment. I saved my skin by getting the job done on time. Thanks for saving my neck! I would have fallen down the stairs if you hadn't held my arm.
save your skin
or save your own skin
COMMON If someone tries to save their skin or save their own skin, they try to save themselves from something dangerous or unpleasant, often without caring what happens to anyone else. It looked to me like a desperate attempt to save his skin. It's an announcement that's got a lot more to do with the government trying to save its own skin than trying to help the victims.