I know in Europe that companies may require a contract once given employment. Well, no airline in the US requires that. Some cargo and charter companies require that you sign a contract for the training they pay for. However, once you receive your training at an airline there is nothing keeping you there. Give your two weeks notice and be on your merry way if you'd like. Now, if you apply for a job elsewhere then you move to the bottom of their seniority list. For example, you are a United Airlines pilot and get furloughed. For some reason you decide to take a job at Southwest Airlines. Well, you are required to give up your seniority number at United as a condition of employment at Southwest. That's usually how things work over here.