Teachers who wish to terminate their contract for any reason must give at least 30 days notice in writing to the school (please check your contract). This is so the school has time to find and bring in a replacement teacher. The employer will be required to pay the employees salary up to and including the date of termination but will not be required to supply the teacher with a plane ticket to their point of origin nor pay any contract completion bonus. If you terminate the contract before 6 months, most of schools require you to reimburse airplane ticket fare that the school provided (Please check your contract).
Hence if you give proper notice stated on the contract then terminating the contract prematurely will not be hard thing. But please make sure that Korean employers always prefer someone who has completed contract and if you do, it helps your salary increased.
After the visa is terminated, you are allowed to stay between 14~30days.
If you have decided to keep teaching in Korea, you have to apply for visa, it means you need the visa necessary documents and give them to new employer. Therefore if you think of terminating contract and work in another school, please prepare the whole document.