What is part of a software program that can be executed independently of the entire program?

Answer 1

You cannot have any one part of a program execute independently of the entire program. What you can do is instantiate a thread of execution that runs concurrently with the main (primary) thread. Concurrent threads are not independent of the primary thread since they all share the same memory, but they each have their own stack.

The only way to execute a completely independent program is to spawn a completely separate process, however separate processes cannot be regarded as being part of the same program, even if they happen to be separate instances of the same program.