Those are excellent questions SolarSippers!
Wine vine roots are similar to other vine roots - they can definitely die if some pest attacks them or if they get zero water or nutrients. They are very strong though and can last out serious droughts.
The roots in Europe are different than those in America - they are a different type of grape. Grapes in the US are naturally resistant to phylloxera - a type of louse we have over here that eats vines (yummm!). The types of grapes in Europe didn't have this resistance. That means when phylloxera was accidentally brought over to Europe, the phylloxera went hog wild and began eating all the European grape vines.
So at this point all the vines in Europe have been "grafted" (attached onto) American root bottoms. That way the louse - which lives down low - doesn't eat the bottoms of the roots which are American. The tops of the vines are still the European style of vines which grow Cabernet and Chardonnay and other such grapes.
It's really pretty fascinating! Most grapes in Europe are now these two-part vines. US on the bottom half, European on the top half.