What happens if someone connects a PoE supplier device in my network (In a single switch port)? Does it mean all my network will offer PoE?
Is it possible to detect a PoE supplier in you network?
You will not have PoE over your network in that case, the switch does not "redistribute" power to the other ports. If you want PoE, you need either:
If your switch support PoE this means it is able to power devices, but you might have to configure it, and in that case, there is no need for an additional injector.
Short answer is no.
The piece of hardware you are referring to is called a PoE injector. It is designed to sit between your network and a the device needing power to inject power for that one device.
Non PoE switches do not have the circuitry to pass this electrical current to all ports. So reversing a PoE injector and attempting what you are surmising would probably result in a dead switch.