I have an employee that has been with us 6 years and we can't afford her right now so we need to lay her off. We want to be able to have her work part time under the "working while on claim" with the intention of hiring her back full time after the 13 week layoff period. If she decides to get another job during this period, do we still have to pay her termination pay?

Unless you have a history of laying this employee off and/or you have a contract or agreement that specifically provides that you can lay this employee off, I would caution you to be careful about moving forward with a plan to lay her off or reduce her hours. Either action might be legally construed as a constructive dismissal, wherein the company would be required to pay her in lieu of notice as if she'd been terminated. I would recommend speaking to an employment lawyer at the number below before acting and to ensure that the company is not unnecessarily exposing itself.