Among the options given, the living being that has a respiratory organ but does not have a brain is option 2 - starfish.
Option 1 - crab: Crabs have both respiratory organs (gills) and a brain, so this option is not correct.
Option 3 - blood succor: This option is not a known living being, so it cannot be the correct answer.
Option 4 - silverfish: Silverfish, also known as fishmoths, have a respiratory organ called trachea and they also have a small brain. Therefore, this option is not correct.
In conclusion, the correct answer is option 2 - starfish, as they have a respiratory system (papulae) for gas exchange but do not possess a centralized brain.