Okay, I’m pretty sure that this is not possible but a client had asked me to do so in one of our Android application we developed for her.
What she had wanted is that if our application is running, and user navigate to:
Settings > Manage Application > [Our Application]
, the button for “Force Stop” is disabled.
Is this possible? If it is possible, could someone point me out which way I should walk, or if it is not possible, how, using a valid argument based on facts, should I break the news to her.
Update:
She just sent me a screenshot that, in her opinion, validates her request that there’s an Android application that disables “Force Stop” button. How am I supposed to explain this to her?

This is not remotely possible, for great reason.
You should tell her that making this possible would be a huge security disaster. Imagine what would happen if you could create apps which just ate at your processor time by holding a wake lock, and you couldn’t kill them. This would be horrible.
In general, if you’re wondering if you can modify the “extra-app” behavior of the device, the answer is usually *no*. You should take the viewpoint that nothing on the device is yours to control besides your app and (to a limited extent) the resources to which you’re granted access.
No other app has this kind of control, so it’s not reasonable to expect that your client’s would either. However, the fact that she’s asking for this control usually implies something else: that they are worried the user will stop the app and then something bad will happen (the locations will stop being synced, data will stop being sent out to the net, etc…). This would imply that you should look into improving the resilience of the app to different situations. Remember, your app can even be killed off at any time by Android (for example, in the case of low memory).