Does it matter if the owner had yet reported the car stolen?
No.
There is no plausible legal theory I can imagine for which this is relevant.
In any case, usually car theft happens and is over before it is discovered.
I suppose the only exception would be that a handful of jurisdictions have at least considered imposing liability on gun owners who don't promptly report their guns stolen upon discovering that they are stolen, for harms caused by the stolen guns. If the car had a gun in it, and the car was stolen and neither the car theft nor the gun theft was reported, in a jurisdiction that adopted a mandatory gun theft reporting law, there could be liability for the gun owner if the stolen gun was not reported and someone was harmed with the gun in the stolen car.
Does liability extend to the owner?
In general
Generally not. The default rule in all but a few U.S. jurisdictions is that the owner has no liability for harm caused by the owner's vehicle if the owner isn't the driver, unless the owner has done something wrongful personally or has a special relationship with the driver (e.g., employer-employee).
According to the New York State Bar Association, New York State (pursuant to NY Vehicle and Traffic Law § 388) and Rhode Island are the only U.S. states which impose vicarious liability (i.e. liability without any fault of the owner or any special relationship with the owner) on vehicle owners for accidents caused by people who drive their vehicles with their permission (which, even then, wouldn't impose liability for an accident caused by a car thief on a car owner). This rule is pre-empted by federal law for rented and leased cars, however, even in New York and Rhode Island. 49 U.S.C § 30106(a). I also don't rule out the possibility that one or more of the at self-governing U.S. territories (e.g., D.C., Puerto Rico, U.S. Virgin Islands, Guam, and American Samoa) have the same rule as New York and Rhode Island.
If the thief injures someone else or property, the theft would usually be as a matter of law a legally unforeseeable "intervening cause" that would interrupt any chain of liability between any negligence of the owner (negligence is te predominant legal theory upon which liability is imposed for car accidents), and the harm done.
Sometimes owners of vehicles can have liability imposed upon them for negligently entrusting a vehicle to someone know to be a threat (e.g. because they are drunk at the time), or because there is a special relationship between the driver and the owner (e.g. employer-employee, or the driver is a member of the same household as the owner). But when a car is stolen, any of these theories of liability are precluded.
Possible attractive nuisance liability
There is also a doctrine, usually applicable to children who are injured while trespassing in swimming pools and hot tubs, called "attractive nuisance" which provides that property owners must take reasonable steps to prevent children from being able to access dangerous things that are particularly attractive to children.
So, if the stolen car were unlocked with the keys in the ignition of a car that looks like a toy or is just flashy, and a child steals it and then the child or others or property are harmed as a result, the doctrine of attractive nuisance could impose liability for negligently failing to take any kind of minimal reasonable precautions to prevent a child without any special car theft skills from stealing the car.
For example, suppose a ten year old gets into your unlocked car in which the key was in the ignition and then drives off with it harming the child and/or other people and property. The car owner might have liability in that situation if a jury found that it was negligent to leave the car unlocked with the key in the ignition when there were young children around.
Possible deadly trap liability
So far as injuries to the thief go, the most plausible analysis is to look to the analogy of a trespasser or burglar who is hurt on real estate owned by someone who is sued. At common law, the only duty a property owner owes to a trespasser is to refrain from putting deadly traps on the property, at least without fair and adequate warning of their existence.
So, if the car owner has outfitted it with deadly traps (e.g. poison gas or a trap that shoots a bullet at the thief or set the car thief on fire), the owner might have liability to the thief for the thief's injuries and to anyone else who is injured by the deadly traps.
Indeed, I saw a news report sometime in the last month or two (it may have been a stale story, however) in which the maker of deadly car alarm traps somewhere in Southeast Asia that sprayed gasoline on car thieves and set them on far was forced to recall this security system from the market.
This said, some states, including California, expressly exempt property owners from liability to certain well defined people committing crimes for the injuries that they sustain while doing so from the condition of the property.
Does it change things if the car was not in good working order?
Only, possibly, in the extreme case of a defect so serious that it is a latent deadly trap that the owner doesn't warn anyone of (e.g. with a sign that says - "WARNING, the car is broken and will blow up if started"), but the defect nonetheless doesn't prevent the car from being stolen.
Usually, if a car doesn't work, a car thief can't fix it either and thus, can't steal it. But I do recall one police procedural TV episode where a car thief did fix a car so it could be stolen.
Footnote: Product liability
A seller or manufacturer of a defective vehicle is usually liable for harms to others caused by the vehicle's defects.
If, apart from stealing the vehicle, the thief otherwise uses the vehicle in the same manner as an ordinary driver of the vehicle might, the seller or manufacturer of the vehicle might have liability for the harm caused by the defect.
Of course, if the thief, as car thieves often do, drives the stolen vehicle in a reckless manner and the way that the vehicle is driven causes the harm, even if the defect contributed somewhat to the incident causing the harm, the chain of causation between the defect and the harm would probably be broken by this intervening cause of reckless driving by a thief which would probably relieve the seller or manufacturer of the vehicle of defective product liability for the harm.
