When Did the Modern Employer/Employee Relationship Come About?

Go back to Bible times, and the only “work” (in the sense of “having a job”) mentioned seems to involve either slavery (Ephesians 6:5), laborers hired just for the day on an as-needed basis (Job 7:1), and merchants (who may or may not have employed apprentices from time to time).

What I would like to know is, is there a point in history where one can say, with some degree of certainty, that the modern practice of employing a person on a paid basis, with the understanding that he/she may continue to return to work for you until either party says otherwise, came about?

What you seem to be describing is factory work. Where separate, possible repetitive tasks, performed by a number of semi-skilled people, all working towards a common goal – to build a plow, produce earthenware, or weapons, for example. Note that “factory” is a very old word, that predates the industrial revolution. Craftsmen may even have used the concept back in pre-Biblical times.

http://en.wikipedia.org/wiki/Factory#History

I didn’t get factory work from the OP.
I just figured (s)he was talking about salaried work, which goes back a loong way.