You cannot transgfer anylonger since you are not in H-1B status currently. You can get a new H-1B visa, however, with the same or new employer. Since you had H-1B status in the past 6 years, you won't be subject to cap so you can apply whenever your employer wants.
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You can apply for a new H-1B visa.
(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
You cannot transfer it since you no longer have the status, but you can apply again (and are not cap subject, so this can be done whenever). Does the company have an immigration lawyer retained? That's probably a good person for you to talk to.
This is not legal advice and no attorney-client relationship has been formed, now or in the future. This is just a casual opinion expressed about a hypothetical situation.