First I answer your questions and then I'll give you more info about my story.
I made a test: There seems to be about 0.9V on the digital outputs when 9V is connected between the CLAMP and GND.
It's not my case, I do not found 0.9V on the digital outputs.
This is normal: The 0.9V is due to the leakage current of the CLAMP diodes in the IC4.
As above, I don't know if it's normal but I understand that the ULN2803 is a very instable and unsecure component.
Is there 9V on the other digital outputs if there is no LED between the CLAMP and the first digital output and you turn the first digital output ON?
Is the 9V there on the other digital outputs only when the first digital output is ON but not if OFF?
YES and while the voltage is on all digital outputs only the led of the first digital output (D1) is on, all others led are off (D2...D8)
Now I tell you about my "apparently" solution.
In order to understand what causes the problem and since the k8055 has two ULN2803, I switch the position of the ULN2803 from IC4 with the ULN2803 from IC2. In this way I get confirm that the ULN2803 that was on IC4 is damaged. In fact, with the right ULN2803 now is all working as expected.
The strange thing is that the damaged ULN2803 that now is on the IC2 socket, is not damaged at 100% because the Input channels are also working as well!
To be sure I have connected a relay board k2633 to k8055 that switches regularly all relay on the k2633 board.
The board now is working and I'm amazed.
The ULN2803 is very sensible component that has strange behaviours when is damaged (looking at my experience and your tests with 9V on CLAMP and GND).
With the k2633 I had problem to switch the second relay but, and again, changing the BC557B from T1 to T2 and BC557B form T2 to T1, the second relay now is working, and the first relay too!
The life is really weird.
Your thought is very important for me, please let me know.