save one's skin, to

save someone's skin

 and save someone's neck; save one's bacon
Fig. 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.
See also: save, skin

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.
See also: save, skin

save one's skin, to

To save one’s life. The skin in question is usually one’s own, and it is hard to imagine life going on without it. The term has been around since Roman times. In English it was in print by 1642: “Equivocating with our conscience . . . for the saving of our owne skin” (Daniel Rogers, Naaman the Syrian).
See also: save