to make sure, Elizabeth is the girlfriend? I am actually watching Back to the Future II... basically you are asking why she is still there even though the past for everybody else has drastically affected their present? Allright.. I will say that because Elizabeth's past (parents' lives etc) weren't involved with Biff nor Marty/Mom's situtation thus the lives of Elizabeth and her family weren't affected by the choices Marty/Biff made in the past. To push it to an extreme form-- Rock n Roll still exist int he present even though Marty Jr plucked the guitar and brought the glimpse of Rock N Roll to an naive 50's audience at the prom... yet the apperance of Elvis and whoever still exists and are remembered int he present. why? because Elvis wasn't involved with marty's mom fighting off biff's sexual advances.
Simple as that. Those who change their own past which only affect those who participate in the process of creating the present, i.e. parents who raise you, siblings living under the same roof.
... [threw in her two-pennies and now turning to watch the remaining of the movie to see if her theory works]
MY ONLY BIG PROBLEMS WITH THAT MOVIE--- HOW THE HELL DOC STILL INVENT THE TIMEMACHINE (DELOREAN) EVEN THOUGH HIS PAST HAS BEEN CHANGED MANY TIMES? Or is it the past AFTER he invented the time machine that have been changed many times? 
Simply mind-boogling movies that are the classics of our times.
