Crime stats do indeed have the obvious problem that when crime is pervasive people stop reporting because reporting just exacerbates the harm of the crime by wasting your time.
One way to deal with this is to look only at murder stats, as there is a lot less reporting optionality there.
Unfortunately, that method is biased by changes the ratio of murders to other crimes. And particularly when the hypothesis is that there is rampant lawlessness and property crime as a result of law enforcement and prosecutors failing to enforce against those less severe crimes, a divergence between murder and other crimes is almost inevitable (unless the failure to arrest and prosecute also extends to murder...).
One way to deal with this is to look only at murder stats, as there is a lot less reporting optionality there.
Unfortunately, that method is biased by changes the ratio of murders to other crimes. And particularly when the hypothesis is that there is rampant lawlessness and property crime as a result of law enforcement and prosecutors failing to enforce against those less severe crimes, a divergence between murder and other crimes is almost inevitable (unless the failure to arrest and prosecute also extends to murder...).