Once the police are called in, basically they decide whether to pass things on to the DA. Then the DA decides whether there is enough evidence to try for an indictment. In the “old days” crimes such as domestic abuse could be prosecuted successfully only if the primary witness, aka “the victim,” was willing to testify. Even then, there was a strong societal belief that somehow the abused person caused what happened to them. This has changed a lot, especially now that so many women work. When the abuser shows up at the workplace, there are plenty of witnesses.
Typically, crimes against property are given lower priority than crimes against people. Thus, rape, assault or murder would be more likely to be prosecuted than theft or burglary.
“should they get away with it?”
No, but this isn’t a perfect world. Even if a case does go to court, there are many reasons why the defendant “gets away with it.” This includes everything from the quality of the testimony and the evidence to the quality of the lawyers involved and the jury. However, it was decided when the United States and other culturally British countries were set up, that it is better to assume innocence and prove guilt, than to assume guilt and prove innocence.