....if an illegal criminal commits a rape in Texas and seeks asylum in Denver, the Denver authorities will not assist ICE or Texas authorities in the extradition back to the state that the crime was committed in. They also won't arrest them.
You claimed Sanctuary policy states illegals serve their time where they committed it....but that isn't really true since in the case being discussed, the Sanctuary City doesn't have jurisdiction over the crime - that would require extraditing the illegal criminal back to Texas. So they don't do anything. Further, the reason that they also won't assist Texas (in this example) authorities in returning illegal criminals is because the fear that those authorities will then get ICE involved for deportation. Thus, the result is that illegal criminals are given a safe haven in Sanctuary Cities.
Sanctuary City policy is policy that provides safe haven to criminals who happen to be illegal immigrants.