The whole phrase is "Brown Russian Roulette." The meaning is taking heroin and a possibility that you will overdose and die just like russian roulette.
Buyer: Dude, can you BRR on this stuff?
Dealer: Hell no man!
Buyer than shoots dealer for being a dealingliar.
Quite simply, a 'Brown Run' describes the hurried scurry to find the nearest Khazi when one feels ‘under pressure’ and is quickly realising that one should really have shat earlier, indeed much earlier !
"Just got back from skiing holiday, no bloodysnow on the black run! I did the blue run tho, anywayz, I've just travelled 300mile down from Newcastle, I'm off for a Brown Run!"