I am wondering that will activity run the method "onDestroy" when killed by system?
for example, when the state of "activity A" is onStop ( user may press the Home button directly ), at the same time, system find out that the memory is not enough so system have to kill some background processes to keep foreground activity alife, say system kill activity A.
Will activity A run the method "onDestroy" in this situation?
It will purely depend on the system condition at that time. Docs clearly says about onDestroy() that:
There are situations where the system will simply kill the activity's hosting process without calling this method (or any others) in it, so it should not be used to do things that are intended to remain around after the process goes away.
See Here