We have a functionality that we would like to be available outside of the app and are wondering of there is a way to launch a small control that lives when the app isn't on, and can be "overlayed" onto any other app.
The control is just a way to help people with disabilities navigate the phone easier using new gestures.
Maybe something with a settings bundle?
What I think you want to look into is creating Cydia Substrate (formerly known as Mobile Substrate) tweaks.
Substrate tweaks allow you to inject code into other iOS processes, including the SpringBoard itself, Preferences.app, or any other app or framework.
In addition, you should checkout Ryan Petrich's libactivator, which allows you to build extensions that listen for different user actions or gestures, and let you respond to them.
This advice assumes you are deploying to jailbroken devices, as your question tag suggests. Without jailbreaking, you won't be able to do much useful in this area.