If you're a non-person, you're absolutely a non-person. It's much like being declared a bandit in ancient Rome -- you have no rights as a citizen, period.
I don't think that's completely true. In Vice, it says that SINless can only be held in custody for up to 7 days. Sure, it's more than double the limit for SINners, but there is some limited protection in the system for the SINless. Of course, it also says that if they have reason to believe that you've given them a fake SIN, they can hold you until they verify the authenticity of your SIN, and as they have no time constraint on that they can effectively hold you indefinitely.
I read that as even the SINless, probationary citizens have minimal rights, but that those rights are often abused.
The larger problem with just opening fire with lethal intent is that LS has no clear way to know (generally) that their targets don't have SINs. And even if they believe them to be SINless, it's dangerous to risk a PR fiasco if it turns out they do have SINs. And, perhaps more importantly for my game, any number of people who may resist arrest or otherwise avoid the detectives won't necessarily be culprits so much as leads. Hard to question a witness if he's dead, SIN or no SIN.
Yeah, a SINless can only be held for seven days...if you take the time to arrest 'im and drag him into the station, creating electronic evidence of them and stuff.

Like so much else, it just comes down to the "feel" of the game you want to play. To the officer in question, it'll come down to what kind of neighborhood he's in when stuff goes down, what kind of day he had, what the SINner/SINless person looks like, what they're doing, what their metaspecies is, how many other cops are around, how many other civvies are around, how many other perps are around...and on and on and on.
But in the wireless age, one of the assumptions is that it's a lot more necessary to have a solid fake SIN, just for everyday travel and stuff. So the implication of that is that it's easier to spot someone with no SIN (real or fake). So if the shit's going down and a high-strung cop hasn't got
any SIN information popping up on his heads-up display, while staring down a group of folks causing trouble, as he sweeps them with his smartlink, facial recognition software, and whatever other goodies you decide a beat cop has?
Well, shit. The most that might come of it, once he starts pulling the trigger, is explaining to the precinct Quartermaster that he's awful sorry about getting it mixed up, the magazine of gel rounds versus the magazine of real ammo, and all...
PR fiasco, PR schmiasco. Sometimes I like my dystopic cops to be, well, dystopic. Sometimes that means they
do shoot now and ask questions later, especially if they don't think the person they're shooting at has any legal rights.