If you find other work and an employer who is ready to apply for your LMO, you can try that. If the employer gets the LMO, you can apply for your work permit. While you don't know if the LMO or work permit comes through, you should continue working in your old job. Once you have your new work permit, you can not continue working for the old employer anymore.
However, if you are under the live-in caregiver program, you know that after 2 years of work, you qualify to apply for permanent residency. If you go out of this program to take other work, you can not apply for permanent residency through this program anymore. If you get a job considered to be skilled, you will have other ways of applying for permanent residency but if it's a low skilled job, it's very hard.
