To my understanding, you need to have two paystubs from the comapny who initially filed your H1B. So it's better to hang out with that company till october end and getting two pay stubs.

Once your H1 status starts with a company and then they fire you, I guess you have 30 days to find another job.

I had a friend of mine, who was laid off in May while his H1 was to start only in October. Although he got a new job [under CPT] in May itslef, he had to work on the new job as a consultant from the older company in October for a month to get two paystubs from the older one, later he transferred the H1 to new employer.

Both were Desi companies, so eth was okay.