For a song
Definition 1 of 1
Pro Tip 1/3Idiomatic Usage
Used especially in informal contexts, but understood widely and acceptable in various situations. 
I picked up these vintage comics for a song at the flea market.
Pro Tip 2/3Figurative Speech
Remember, 'for a song' is a figure of speech meaning very cheap - it doesn't involve actual singing. 
The antique clock was sold for a song at the auction.
Pro Tip 3/3Metaphorical Value
The phrase suggests something's so cheap it's almost like trading it for a simple song. 
They're giving away the old stock for a song to clear space.