I want to do something on app start if the app is closed unexpectedly last time.(crash, force close), how can I tell it?
Yes, you can do it: the simplest way is to create a file with a known name in the directory, and delete that file upon the "normal" exit. If the file is there on launch, you know the previous exit has not been a "normal" one.
You could update the content of the file periodically, writing the current timestamp on a timer every minute. This way you would know approximately when the abnormal exit has happened.