He wrote the story with his friend's 'assistance'. = He wrote the story 'with the assistance of' his friend. [=his friend helped him to write the story]
Our family had to 'go on public assistance' [=receive money from the government] when my parents lost their jobs.
Nobody 'came to her assistance' [=nobody helped her] when her car broke down.
(..) Are you... Are you all right, sir? - Oh, yeah, I'm OK. - You look terrible, sir. What happened? - Nothing, it's no problem. - No, no, no, sir. He's not kidding. - You look awful. You need assistance. - I'm fine. Look, I'm fine... Everything's fine. Stop it! - Let her go. - Christ Almighty! (..)1999 Fight Club