This may help make the issue a little more concrete. I don't know how often illegals commit crimes like homicide, but i hear about it fairly regularly... the actual numbers should be available somewhere.
REQUEST FOR STATEWIDE REBROADCAST
LAW ENFORCEMENT OFFICERS KILLED IN THE LINE OF DUTY-2007
PART 1 OF 1
KENOSHA COUNTY SHERIFF'S DEPARTMENT, WISCONSIN,
ADVISED VETERAN DEPUTY SHERIFF, AGED 48, WITH 18 YEARS'
LAW ENFORCEMENT EXPERIENCE, WAS FATALLY SHOT AT ABOUT
11:37 P.M. ON 05/16/2007. DEPUTY ATTEMPTED TO INITIATE
TRAFFIC STOP ON SUSPECTED INTOXICATED MOTORIST. DEPUTY
BEGAN TO PURSUE SUBJECT, WHILE UNIVERSITY OF WISCONSIN -
PARKSIDE POLICE DEPARTMENT (UWPPD) OFFICER WAS
ATTEMPTING TO JOIN PURSUIT AND ACT AS COVER FOR DEPUTY.
AFTER APPROXIMATELY 15 BLOCK LOW-SPEED PURSUIT OF
SUBJECT VEHICLE, WHICH ENDED IN CUL-DE-SAC, DEPUTY
EXITED PATROL VEHICLE AND STARTED TO APPROACH SUBJECT.
(UWPPD OFFICER WAS THEN ATTEMPTING TO OBTAIN ADDRESS OF
TRAFFIC STOP.) EXACT DETAILS OF OCCURRENCE ARE
CURRENTLY UNKNOWN; HOWEVER, IT IS BELIEVED THAT WHILE
DEPUTY WAS APPROACHING SUBJECT VEHICLE, SUBJECT EXITED
AND BEGAN FIRING .380 CALIBER HANDGUN TOWARDS DEPUTY,
FATALLY WOUNDING HIM IN FACE. VICTIM DEPUTY RETURNED
FIRE. AFTER BRIEF GUNFIGHT BETWEEN VICTIM DEPUTY AND
SUBJECT WAS OVER, UWPPD OFFICER FIRED AT FLEEING
SUBJECT. THREE HOURS LATER, SUBJECT WAS ULTIMATELY
ARRESTED SEVERAL BLOCKS AWAY FROM INCIDENT. KENOSHA
COUNTY TACTICAL RESPONSE TEAM LOCATED SUBJECT HIDING
BETWEEN TWO CARS. SUBJECT WAS APPREHENDED WITHOUT
INCIDENT AND WAS FOUND TO BE IN POSSESSION OF WEAPON
USED AGAINST VICTIM DEPUTY. SUBJECT WILL BE CHARGED
WITH FIRST DEGREE INTENTIONAL HOMICIDE. ADDITIONALLY,
SUBJECT IS BEING HELD ON DETAINER FROM U.S. BUREAU OF
IMMIGRATION AND CUSTOMS ENFORCEMENT FOR BEING IN U.S.
ILLEGALLY.