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1.
UK useage.

The police in an area notorius for it's highcrime rate eg Whitechapel in East London, The Barton Hill area of Bristol, Bootle in Liverpool, the cornish town of Bude etc.

So called because said police see themselves as the only thing preventing an out break of anarchy
With 19 muggings, 34 assaults, 4 street fights, 7 car jackings, a rape, a murder and only 6 police the thin blue line is being streached tonight.
by black flag June 02, 2004
 
2.
the banding of all cops in any state despite right or wrong. The reason why NYC police only have cameras in their highway cars
All police rely on the thin blue line
by Anonymous November 01, 2003