save (one's) own skin
To rescue or protect oneself from danger, trouble, or difficulty, especially without concern for the welfare of others. In the face of the federal investigation, the CEO was more worried with saving his own skin than ensuring his employees' jobs remained secure. Just be sure not to leave yourself exposed in this scandal. You can be sure that the senator is looking to save her own skin, so you should be doing the same.
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.