Work visa transfer

Hello blind community, I have a question regarding my visa status. I was effected in mass layoffs in december 2019 and I found a staffing firm who actually gave me a temporary/short term role while they support my visa transfer and payroll. My question is, lets assume I find a full time job while my visa application is in process, do i need to tell this new company about my pending application ? If at all i dont , when they ask about how I am managing after 60 day grace period i then have to provide them my new pay stubs. Will this situation put me in the verge of not offering full time by the company ? Please let me know. Appreciate your suggestions. #h1b #layoffs