The history log is not cleared by default. That means it can be used to store and lookup information about completed process instances. Based on the start and end date, you can derive whether is it still active or has been terminated. You can even find out more by looking at which nodes were executed (to detect for example normal completion vs. error).
Note that the history log could also be considered an example of how to store history information. You can easily tweak it to store more or less information, etc. as it is based on a simple listener approach.
Kris