Kaliningrad

[Joe Republic]

After the Allies redrew Poland's borders after WWII, the German city of Konigsberg was separated from the rest of Germany.  Because the separation of Prussia from its motherland was one of the reasons why Nazi Germany had invaded Poland before, it was felt that it would be easier to take Konigsberg away from Germany completely.  At Potsdam, the Allies agreed to give the city to the USSR, who changed its name to Kaliningrad.

[Joe Republic]

But why did it remain part of Russia after the USSR split up?

What J.J. said.

Also, the province was put under direct control of Moscow, whereas the other countries within the USSR were granted very limited autonomy.  When the USSR split up and the other countries gained independence, it was just felt that K'grad couldn't really sustain itself.