An application, that doesn't "belong" to a user, but to the system is called a service in NT (so also W10) parlance. While it can't provide a UI directly, it can create an endpoint where a UI-only application plugs in to show a UI.
This is best explained with the Windows Update mechanism or the Windows Defender mechanism: Both have a worker process running as services, i.e. in the Background decoupled from a User being logged in, but their UI is seperate from this worker process and doesn't keep any state - it can be killed without affecting the underlying service.
The UI process connects to the worker process to get the state of the service and display it in a nice UI, or to send commands to the service which were entered via the GUI.
If your application does something "fancy" that needs UAC consent, this model also helps you: Services have intrinsic consent (the UAC popup i/a comes when installing it), and the UI part doesn't need it.
Please add more details about your application and scenario. Why don't you just have you users RDP to the certain computer with the same credentials and never log out? They can disconnect the session and leave the software running. – simlev – 2018-09-28T08:55:57.370
They need to be different users as they have different permissions to some folders, etc. – Recon – 2018-09-28T09:05:28.193