Yesterday I watched a video "How to connect LED strip to your car" in which one of the LED powering cable wires was connected to the body of the car(grounded) and the other one to a fuse. My questions are: What is the flow of the current? Is there a way for electricity to go through a consumer without a return wire? What arose my curiosity was that, if I am right, when grounding occurs there is still a return wire for the electricity and the ground wire is in case of an electrical fault to prevent the metal surface of an object to conduct electricity. However, in the case, I mentioned above, the electricity will flow through the body of the car if it is the return wire. I would really like to hear an explanation from you because I wish to install my LED strip sooner. Thank you in advance.
@MaxW is correct: the metal chassis of the car furnishes the return path and a separate wire is not required. The only exception is for loads which carry very large currents; in these cases a separate heavy-gauge copper ground return wire or woven flat braid is used between the load and the negative clamp on the battery.
Since the car's bodywork is the return wire, you'll have to be sure to establish a good metal-to-metal connection between the LED strip ground wire and the car body. Those ground connections are a common source of trouble in car wiring systems, especially if the connection is made not at the factory but by the owner who is adding some circuit to the car!
Here is a schematic wiring diagram for a car which shows the use of the chassis/frame as the return path including the high current battery to starter motor connection.
The chassis is most often, but not always, connected to the negative terminal of the battery so this needs to be checked before connecting your device.
Making a new earth connection to the chassis should be done with caution as it will potentially expose metal to the elements and accelerate corrosion, so it is best to use existing connections.