As dresposa has chosen to ignore me, let me ignore her fantasy anf give the real world reality of bringing an alien worker to the US. Firstly we are talking about a typical situation, not a world-class baseball player.
First you must try to fill the position by an American worker. You must prove this by advertising the position in US newspapers, including job description, pay, etc. There are very specific requirements, which is why an attorney is usually necessary. Once you prove that you cannot hire somebody already in the US you can apply to sponsor a foreign worker. This foreign worker, if approved, is sponsored for a period (I believe 3 years by the employer). If approved you wait for the next available slot in the quota for the country of origin. In the case of the DR you will wait a very, very long time. In practical terms, a person from the DR will never receive a green card to work in the US for an unskilled position.
The question of contract is covered in the application process. If the job terminates early, the person must present for deportation as the approval was for the job, not the employee. There is an appeals process the worker can use if they feel they were terminated unjustly.