Idiom or Expression related to Nepotism

Have friends in high places is close to what you are looking for:

• to ​know ​important ​people who can ​help you get what you ​want.

Also: a person with connections:

• connections [plural]: the ​people you ​know and who can ​help you:
  • He only got the ​job because of his connections! He has ​important connections in Washington.

(Cambridge Dictionary)

I like the phrase

He's untouchable.

Meaning: Not subject or susceptible to criticism, rebuke, or attack: an appointee who was untouchable because of his political connections.

Kicked upstairs

kick somebody upstairs to give someone a new job which seems more powerful but is really less powerful, usually in order to stop them causing trouble for you. Brown is being kicked upstairs to become chairman of the new company.

kick upstairs. (n.d.) Cambridge Idioms Dictionary, 2nd ed.. (2006). Retrieved March 27 2016 from http://idioms.thefreedictionary.com/kick+upstairs

We used to call people in that situation "asbestos" in other words: fireproof.