What happens when a high power LED shorts in a LED series string?

Hello. I'm learning about high power LED's. I would like to design a high power LED driver for a DIY project I'm working on. I'm planning on using an LED driver to provide constant current and have dimming control through PWM. I'm going to be using 3W high power LED's in a series configuration. I will have about 12 LED's in series. From what I understand the LED driver will adjust its output voltage to keep the constant current. The question I have is what would happen if an LED was to short? I'm assuming that the output voltage of the driver would be lowered to get that constant current but I'm not 100% sure, so I thought I would ask.



I think I might use a LM3404 to create the constant current driver but I'm not sure.