Resignation from company after I797 but before stamping

Hi.

My H1B I129 PETITION is approved in 2014 lottery in this July. But my visa has not been stamped as the position for which my current company applied for, that has gone on hold. Thus the stamping might not go through at this time. I’m planning to change the job and join another Indian IT company in which there is no US work.

  1. If I resign from my current company, will my current company inform USCIS that I have resigned and then my I797 will be cancelled? I read that most companies do it to safeguard them from some future liability. And for this cancellation, will the current company have to spend some money for cancellation, or just by informing the USCIS will be enough for them?

I just have the I797 copy with me but the stamping hasn’t been done.

I want to move out from the current company but at the same time, don’t want to lose the H1B as well.

Please advise.

Thank you.