Is that the case? Bitcoin if it dies. I do not think the other coins will go well.
It solely depend on what is the caused why bitcoin dies?
If bitcoin dies due to the lack of user because people lost interest in it for the reasons of high fee and slow transaction this event will give other coin a chance to become big in the market.
If bitcoin dies due to banning and being regulated by the government around the world then the chances of other coin to follow the path of bitcoin is surely 100%.
Different events will lead to different results, these occasions may happen in the future and lets no forget that South Korea and China are taking a step against bitcoin and alt coins today.