I've read here that running the TLC5940 with no load can cause some issues with it drawing excessive power. The TLC5926 is a constant current driver rather than a PWM driver. It seems to me that since both of these chips have the ability to detect an open condition on any of its drivers it ought to do something intelligent with that information (like not try and sink current from that driver). Is the TLC5926 susceptible to the sane effect described in the e2e forum post with respect to the TLC5940? What is one supposed to do to deal with this phenomenon?
While the Datasheet for the TLC5926 doesn't address this, and the internal topology isn't explicitly stated, the TI Engineer on the forum post gives what essentially is the same way to deal with the phenomenon:
Of course, since the TLC5926 is a constant current on/off shift register, you can't program it to sink 0mA. You can how ever, simply turn off that individual(s) output if no load is connected. This would be the same way you would deal with a open-load detection.
Your system should check for the open or short circuit detection register, and disable the output as needed, in code.
As for knowing if the TLC5926 does have a higher no load current draw, you could, before connecting the LEDs (Or cutting the V+ to the leds), turn all outputs on, and measure the current draw, then connect the LEDs, and turn all the outputs on, and measure again.