Report the item as stolen and move on with your life.
And all that solely to spare the attacker the consequences of his choices. I'd rather err on the side of the victim here - they didn't choose to be in that position, they were placed in it by actions of the attacker.
Note that this all only applies when the person defending themselves is in a position where they reasonably believe that they're in danger. It's generally not legal to defend your property with lethal force in US, if you are not endangered yourself; the sole exception is Texas.
A more important question is why. We're discussing a situation with a premise that we have already firmly established that the victim was violently attacked, or had a credible threat of the same (if we haven't, then it's not self-defense by legal definition). At that point, why would you accommodate the attacker at the expense of the victim, so long as victim remains threatened (again, if they're no longer threatened, then it's legally not self-defense)?
I often hear truisms such as "every life is valuable", but that goes both ways, and there's no way to avoid judging the relative value of victim's life versus the attacker's in this situation. Since it was attacker's choices that create this contradiction in the first place, I believe that they're fully responsible for it - i.e. the victim has no obligations whatsoever to think about the attacker's safety, only about their own and that of bystanders. Which means removing the threat by the most efficient way possible, rather than the most humane towards the attacker. Once attacker is no longer a threat, then considerations of the value of their life etc are back in force, because it's no longer at the expense of danger to someone else.
Safer for you, right then (unless you, you know, actually need that money, for food). Unsafe for all of their future victims, whom you have just chosen not to help. This is true for the same reason that evolution and game-ification works... Applying positive feedback to an action increases the likelihood of that action being performed again. By giving in, you choose not to stop them, and communicate to them that what they are doing is okay.
Sometimes "safely escaping" is not something you have the time or option to even consider.
It's simply about the human right to defend one's own life.
It would also be a major incentive for the carjacker to carry a gun and possibly use it.
I would think the incentive is that they don't want to die for a car or they don't want to commit a crime someone will actually investigate (a murder).
It's not illegal to defend yourself, but it might be illegal to defend your property, yes. I think it's an complicated moral question whether or not it's fine to shoot someone stealing your TV, but there are lots of practical reasons I think it's probably best to have it generally not be legal.
There's a reason why the United States is such a violent country, and one of the most violent where law & order haven't broken down. I'm not saying I disagree with your sentiment that one should be given some liberties in meeting aggression with aggression. It's how I feel, too. (And I'm not shy around guns, FWIW.) But that feeling was nurtured by our violent culture. In most other countries people don't feel a compunction to buy a gun or otherwise arm themselves after being burglarized or carjacked. A predisposition to resort to violence isn't universal, not among developed nations, not even for defense. That took me awhile to wrap my head around, but IME (Ecuador, Mexico, Malaysia) it's true, even in countries with significantly more violent crime than we have.
The big problem I see is the easy availability of guns, which has turned into an arms race of sorts. So victims (such as for carjacking, the subject here) have very good reason to fear that attackers are armed with deadly weapons, and so many people want to carry guns themselves to defend against this, and so the criminals carry guns too.
In other developed nations, there's generally no easy access to guns, so a victim doesn't have such a large reason to fear for their life. The worst thing they have to worry about is usually being stabbed with a knife, which is generally much more survivable. So these countries generally have much less deadly crime, though they have more petty street crime (pickpocketing or purse-grabbing for instance).
Countries where they have more violent crime like Mexico, El Salvador, etc. are ones where law and order really have broken down, and these aren't "developed nations" either; poverty and crime are both rampant there.
I just think it's important to understand that ours is a rather unique culture. Arming oneself is a reasonable response given our cultural values, and I support Americans' right to own firearms for self-dense (albeit with more regulation than commonly required). I hesitate to say it's reasonable in light of our violent crime. Middle-class Americans suffer very little violent crime. The ones who suffer the most, such as in inner-city ghettos, are communities that most vociferously support gun control and the most skeptical of self-defense arguments. But in any event most other cultures take a polar opposite view--that even aggression in self-defense is to be disincentivized--and I appreciate that it's also reasonable.
If police aren't a deterrent from car theft (as carjacking is a pretty common crime), then we are encouraging that behavior by doing nothing and calling the cops. Conversely, if the average person, during an attempted carjacking, opened fire on the attacker, it would be a major deterrent. There would be almost no repeat offenders (I have been shot at, and it is terrifying).