How can I continue my work permit and visa without going to another country if I change my employer?

A work permit is issued for a specific job, a visa is issued for a specific person

A work permit is issued by the 'foreign employment division of the labor department and social welfare ministry' for a specific foreigner, allowing the foreigner to do a specific described job, for a specific employer, at a specific location. When the job ends you cannot take the work permit with you and your current employer must officially terminate your work permit. When you find a new job in Thailand your new employer must again apply for a work permit, but your current non immigrant visa is not terminated and you can use this for the new work permit application.