a magazine/newspaper 'subscription' = a 'subscription' to a magazine/newspaper
You won't find this magazine at newsstands. It's sold only by 'subscription'.
She bought a 'subscription'. = She took out a 'subscription'.
(..) For a while there, I was attracted to you Well, wait a minute That changes everything They wouldn't renew my magazine subscription because of money I can't believe it Ha ha ha! Martin, would you excuse us for a minute? (..)1987 Broadcast News