Prosecution, you mean "just stay inside and we'll send someone out to take pictures and fill out the paperwork sometime sometime tomorrow."
In a disarmed society, an increase in the burglary rate will reduce the percentage of burglaries that result in prosecution. The reduced risk of prosecution will make burglary more attractive, pushing the rate up further.
In an armed society, an increase in the burglary rate will cause more people to arm themselves, which will increase the likelihood of a burglary being fatal. This in turn makes burglary less attractive as a career choice, and helps keeps the burglary rate in check.