Modules of 3 LED
Simple LED strips or bars that are using 12V input voltage often have the following layout:
They consist of modules with 3 LED each, all connected in parallel to the input voltage.
A single module consists of three LED and one resistor in series with the input voltage.
(This answer has an example picture and schematic: Cuttable 12V LED strip)
High resistance after one LED breaks
The whole module goes dark, and all other LEDs get a tiny bit brighter because they no longer share the power supply and it's connections resistance with the broken module.
The secondary damage here is that more LED stay dark than are actually broken.
Low resistance after one LED breaks
Then, one module consists of only two LED and the standard resistor, which is now way to small for limiting the current in the normal way. So the two other LED in the module ret much more current, and are possibly much brighter. The other modules should get a little darker, because they need to share the power supply with the broken module, which now uses more current.
The secondary damage here is that the two LED which get higher current will break soon too. In the end, more LED will stay dark than were actually broken - because they broke too, in this case.
Of course, in both cases, repairing would mean replacing the broken LED.
But what do to best, in each case, if no replacement LED is at hand?