Why is there an entertainment company behind every Korean star? What is the relation between the company and the Korean stars?

Not all the stars work with companies. There are some who operates individually and hire staff directly. Under this case, 'star' becomes business entity, who needs to file various paperworks for tax purpose. At this level, specific individual successfully established the company with payroll and permanent employment.

For others, there are tons of perks by working with good companies. Management will take care of one's schedule, accounting will do all the works regarding money and expense, PR would work on the materials to publish and secure various roles and performances opportunities, and legal department would protect the 'star' from harassment and such. Only thing the 'star' has to do would be following the schedule, show up on time with good manner, perform at maximum condition, and collect the compensation.

For those girl/boy groups, it is the company who developed the initial idea. Leaving the company and running independently would mean one needs to cover all the works that have been done by numerous professionals in each field, while paying them off from gross income. Not to mention the network the company provided won't be available, either.

Summary:

The company basically hires the idol. From the time they’ve made it through the audition, they are basically in the company’s care. The company provides for their living (unless they live close to the entertainment building, in that case I’m not sure what happens), education, and training.

Basically being signed under the label (the entertainment company) means that you “work” for the company. Part of your earnings will always go to the company until you’ve paid off your debt (training/living/education/etc. cost).

The company essentially owns you.

Info: quora.com