The operating system may interrupt or suspend a thread at any time. This is completely normal, e.g. to ensure that multiple threads can share one processor (pre-emptive scheduling). When a thread is scheduled to continue, the operating system will restore the thread's context, in particular: the virtual address space of the thread's memory, and any CPU registers. The thread cannot tell that it was suspended because it's exact state was restored, though of course time has passed in the meanwhile.
This process model is used by all Unix-family systems incl. Linux, and by extension also Android. For further info on the process model, you can read these lecture slides I found: http://www.cs.kent.edu/~farrell/osf03/oldnotes/L06.pdf
Before a device enters a suspended state, the operating system will suspend all running threads – but the details will depend on how that device suspension works (which components will be powered down).