I don't think if bitcoin dies the rest of the family will also die because some of the Altcoins have different features, advantages and anonymity implementation than bitcoin. Some coins categorize themselves as currency and some as an asset. So, you see because of that they don't serve the same purpose they both have their ways if you know what I mean. Bitcoin is like the father of the family and you know when the father dies the children will grow they won't die too 
Each alts project intended to replace or to back up bitcoin lapses, so just in case bitcoin completely falls, there's another option to move forward, each project have its own offers, most of the quality and real alts create uniqueness, though each of them really relied with the current bitcoin value, who knows after some year one of them will jump high and replace bitcoin, future is not ours to predict let just wait and see if what will happen after.