That begs the question, since death didn't enter the world until after their sin, could Adam have laid down his life for her sanctification?
ahhh...literal interpretation man (that was a character on Whose Line is it Anyway...loved that show)
Husbands are called to love their wives as Christ loves the Church. This call follows directly the call for wives to obey their husbands, which tend to get a lot of attention, which is odd because men actually have the harder calling, but I digress. This means that they are called to sacrifice themselves, not necessarily life itself, but to give fully and completely of themselves.
Adam was called to love Eve this way, he ought to have been willing to lay down his life, to give completely of himself for her protection. It's not that he had to die, but he was supposed to protect Eve at all costs. Which makes sense when you read it because well, I didn't call her "Barbieve" for nothing when I read it for school. The gal needed all the help she could get.