Is there a way to force my application to run at the background This is not a duplicate of this question - Is there a way to force an app to remain running in the background no matter what? because it mention about Android ver 4 and also about lack of memory.

My question is is there a way to force a particular android apps for Android version below 4 to run in the background when the phone is sleeping? Also, I should be able to call those android apps that I specific to run in the background to come to the foreground for me to interact with.

The problem is that some apps, they stop working when the phone when to sleep (due to power saving). Some apps even prompt errors. However, I need them to run in the background. Also, I know that I can use 'Force close' to force a apps running in the background to stop but I just could not find a way to make a particular android apps to run in the background whenever I needed.
It's up to the developer of an app to specify what it should do in the background. Apps have two kinds of component. (Actually, there are more kinds, but they're irrelevant to the question.)

The first, activities, can display on the screen, and can only run in the foreground. However, when you leave an activity with the home key, it gets an opportunity to save its state, so when you next run the same activity, it can appear in the same state you left it. (For example, an email app might display the same email you were looking at before, instead of going back to the inbox.)

The second kind, services, run in the background, and don't display on the screen. They have to be written in a different way to activities, to make sure they don't run down the battery, and they have some control over when they start and stop running.

If an app doesn't save its state, or gives an error when you come back to it after using a different app, you should report that to the developer of the app, so they can fix the bug.