Exobriddian was a drug that was addictive and withdrawal could be fatal. Keiller noted that it was used in "psychological tests for security", but also apparently taken, probably illegally, by others.
Dayna was supposed to fake withdrawal symptoms as part of the plan to steal the Earth-bound gold from the Space Princess, but a change of ship's doctor forced her to take the drug for real. Dr Slaten noted that Dayna would not be given drugs on Earth, suggesting that exobriddian was illegal on Earth if not elsewhere. Reference was also made to "exobriddian poisoning", suggesting that exobriddian might have been a withdrawal-related by-product rather than the name of the drug itself. (TV: Gold)