H1B Transfers don't count against the H1B quota. If you still have time left on your H1B (i.e. approved I797 petiton) and have not violated the 'leave immediately if out of job' rule, it is possible to have a new employer file a petition for transfer of the I797 (H1B)

In fact, in such cases, you don't even need a new visa stamp for the transferred H1B. As long old H1B stamp has not expired, you can present this H1B along with the approved transfer petition and they will let you in.

This is just my understanding of the process and does not constitute legal advice. I am not an immigration attorney or any such. Just a technology guy -:)