limits of copywriter services !

[matrix221]

Hi, I'm new here and forgive me if you find this question stupid but when the job of a copywriter starts and when it ends ? which mean when I cold reach some business, how do I convince him to use my services if those services are only converting readers to customers and not bringing customers from beginning ?
that leading us to the next question, as a copywriter, should I pick business that already have a lot of traffic ?
Thank you guys !