If a person finishes working with Company A under H1B, they get 60 days 'grace period' to find a new employer. When they get a new job offer, they submit the visa transfer application, and receipt of the application by USCIS is enough for that person to start working at Company B. That visa transfer may take somewhere in the region of six months to complete, but the person can still work for Company B.
My question is: if this person finishes working with Company B AFTER the 60 days grace period is over, but BEFORE the visa transfer is complete, do they get a fresh 60 day grace period, or are they immediately out of status upon finishing with Company B?