I agree that the title is not very clear. However, giving the author the benefit of the doubt, I guess what they're trying to say is "protect my H-1B and [my e

I agree that the title is not very clear. However, giving the author the benefit of the doubt, I guess what they're trying to say is "protect my H-1B and [my eventual eligibility for a] green card [that stems from my having an H-1B visa]". In other words, lose the H-1B, lose the chance to get a green card.