I cannot figure out how the system in the car recognize bulb damage via the CANbus. The light bulb is only powered from the battery when the relay is on. But where is the communication bulb (->) CAN -> microcontroller -> computer -> error on dashboard? How information about low current in light wiring flow through CANbus?

 

The circuit might have a lamp current sensor (module) somewhere to detect changes from the expected current draw instead of just a switch. This module communicates with the CANbus.

That module might be inside the lamp.
https://www.superbrightleds.com/blog/can-bus-led-bulbs/293/

 

Make/model/year will yield more answers. Generally a module will detect a difference in expected voltage/current from that circuit and compare it to expected. If out of range, it is flagged as a fault. . May not be related to CAN bus depending on vehicle.

 

I cannot figure out how the system in the car recognize bulb damage via the CANbus. The light bulb is only powered from the battery when the relay is on. But where is the communication bulb (->) CAN -> microcontroller -> computer -> error on dashboard? How information about low current in light wiring flow through CANbus?

CAN Bus is a type of network commonly used in motor vehicles, nothing special in that. Most modern vehicles do not have a separate wire for each warning lamp, gauge or signal on the instrument cluster . Instead the required information is received in bulk as a digital signal sent through the CAN Bus network from various modules scattered around the car. Examples are airbags, ABS, engine information etc.
Again to reduce wiring and size of switch contacts and voltage drop , most vehicles control lighting and signalling (indicators, brake lights horn etc.) using tiny signals , often digitised at source to electronic modules which control the final power output stage, through transistor switching.or relays. These are generically known as "Body Control Modules" , though each manufacturer may have their own name for it.
An added bonus of using electronics for switching lights and other loads is that it is very easy to detect the load current of each individual lamp in the external lighting system. Once a bulb blows or suffers from a bad connection the module can immediately detect it and relay that information through the CAN Bus to the instrument panel and alert the driver.
Bulbs blow and have a limited life Thus many vendors sell LED lamps designed to fit in the same bulb holder as an aftermarket replacement. LED "bulbs" have a far longer life and are a better option. However a typical LED lamp draws far less current than the corresponding incandescent bulb and the system will detect that and register a fault. To overcome this problem , some suppliers of these LED "bulbs" include a built in load resistor so that the current draw is the same as the original bulb and the system does not detect the difference. Such LED lamps are often described a "CAN Bus compatible" or "CAN Bus Ready". They are not directly connected in anyway to the CAN Bus but simply are compatible with bulb failure detection systems.

 

Most LED replacement come with the label........"for off road use only". This includes license plate bulbs and back up lamps. Here in PR, the brighter the better, including full width light bars.