That is the key to start a domino effect. Once the criminals move en mass to nearby counties, their sudden concentration will cause exponential rise in housing problems, crime, drunk driving, ER shutdowns, etc.
The "tolerant" citizens will start grumbling and demanding similar anti-illegals laws, which, upon passing, will create a much larger problem for the next nearby "sanctuary" cities and counties. The influx will not be "tolerated" because of the shear numbers and the above scenario will be repeated even faster.
I bet you, during these county-to-county migrations, some of the illegals will run out of money and places to live and work. Unemployment in the illegal population will increase astronomically to the point that they have to leave the country and go home.
Putting pressure on the "sanctuaries" will eventually solve the problem before violence is triggered, hopefully.
Self deportation through attrition, by cutting off the benefits, penalizing workers, asking for proof of legality to use services, etc. will have a chilling effect and since they never assimilated in the first place, with no allegience to this country, I would predict they will be discouraged, disheartened, longing for home, and they will get the hell out.