There are case studies of this.
I will tell you exactly what will happen;
First off government is going to see 50%+ staffing reductions starting in September, the cops are going to get even a larger cut than 50%. Your local governments are already effectively unfunded and in a broken state. Cops across the state have been told not to contact people, not to write tickets or arrest anyone if they can help it. Every piece of paperwork generated cost money to process, every person arrested cost money to process and incarcerate, money that they do not have. There is a budget crisis across the state.
With all that being said the criminal justice system is unfunded just as the rest of government is unfunded and is for all intensive purposes non functional. The people will find out soon enough.
At first there will be a surge in crime, lasting for a couple weeks. Once people figure out the cops are not coming they will re-assert their own power and take matters into their own hands. When this happens the people will start killing criminals for even minor offenses, keep in mind the "people" don't have less than lethal tools nor do they offer "due process".. Once the criminals figure out the rules have changed most will stop committing crime, some will form larger groups/gangs and form criminal networks "organized crime", which will seek to form partnerships with the people rather than go to war with them. You will see organized crime take a role in policing.
In a nutshell crime will go way down in a short time after a big crime surge. Guns will not be taken, do you think anyone would allow government to come in and sieze firearms now? After the shitshow abortion state and local government has put on over the past 4 months? Do you think most people would trust our state government after what they have done? I think people are going to become much more conservative after this, guns will be integrated into society even more than they are now. Way more people carrying guns in the future.