Are People Allowed to Use Deadly Force to Defend Property?
It depends, whether as to looting or other threats to property.
I touched on this briefly in my looting/shooting post, but I thought I'd elaborate a bit more (especially since the commenters seemed to be interested in both the legal and moral aspects of this question). Note that this is, as usual, not specific legal advice, but just a general layout of how various American courts deal with the matter; many of the rules, as you'll see, vary sharply among states, and often turn on specific factual details. (I say "you" below for clarity and convenience—I hope none of you has to actually do any of this.)
[1.] In all states, you can use deadly force to defend yourself against death, serious bodily injury (which can include broken bones and perhaps even lost teeth), rape, or kidnapping, so long as (a) your fear is reasonable and (b) the danger is imminent (requirements that also apply to the doctrines I discuss below). For instance, you should be able to use deadly force against someone who is trying to burn down your home, since that threatens you with death or serious bodily harm. You should be able to do the same against someone who is trying to burn down your business, though with possible limitations involving the duty to retreat in the minority of states that recognize such a duty.
But in nearly all states, you can't generally use deadly force merely to defend your property. (Texas appears to be an exception, allowing use of deadly force when there's no other way to protect or recapture property even in situations involving simple theft or criminal mischief, though only at night, Tex. Penal Code § 9.42; see, e.g., McFadden v. State (Tex. Ct. App. 2018).) That's where we get the conventional formulation that you can't use deadly force just to defend property.
[2.] This conventional formulation, though, omits an important limitation: In basically all states, you can use nondeadly force to defend your property—and if the thief or vandal responds by threatening you with death or great bodily harm, you can then protect yourself with deadly force. So in practice, you can use deadly force to protect property after all, if you're willing to use nondeadly force first and expose yourself to increased risk.
And in some states, you don't even need to expose yourself to such increased risk, if you reasonably fear at the outset that nondeadly protection of property would be too dangerous. In those states, to quote the Model Penal Code formulation (which some have adopted), deadly force can be used if
the person against whom the force is used is attempting to commit or consummate arson, burglary, robbery or other felonious theft or property destruction and either:
[a] has employed or threatened deadly force against or in the presence of the actor; or
[b] the use of [nondeadly] force to prevent the commission or the consummation of the crime would expose the actor or another in his presence to substantial danger of serious bodily injury.
Note the requirement, in at least this version, of felonious theft or property destruction.
[3.] And that's just for garden-variety theft and property damage. When the theft or vandalism is aggravated in certain ways, many states allow for still more deadly force.
[A.] In about half the states you can use deadly force against robbery, which generally includes any theft from the person that uses modest force or a threat: "Even a purse snatching can constitute a robbery if the victim simply resists the effort to wrest the purse away." Some robbery of course does also create a reasonable fear of death or serious bodily injury, but in these states such a fear is not required.
[B.] In some states, there is a rebuttable presumption that you reasonably fear death or great bodily harm—and may thus use deadly force—if the target is (to quote the Iowa statute),
Unlawfully entering by force or stealth the dwelling, place of business or employment, or occupied vehicle of the person using force, or has unlawfully entered by force or stealth and remains within the dwelling, place of business or employment, or occupied vehicle of the person using force.
This is just a presumption, but to rebut it the prosecution would generally have to prove beyond a reasonable doubt that you didn't actually reasonably fear death or great bodily harm in such a situation.
[C.] [UPDATE 6/2/20 11:14 am; added this subsection:] And in some states, it is categorically permissible to use deadly force against burglary—often defined as entering a building illegally with the intent to commit a crime (including theft) there—or against arson, even when you have no reasonable fear of death or serious bodily injury to yourself. For instance, here is one of the New York criminal jury instructions, which generally summarize several relevant New York statutes (brackets in the following text are in the original, and indicate text that is included if the facts of the case fit it):
Under our law, a person in possession or control of [or licensed or privileged to be in] a dwelling [or an occupied building], who reasonably believes that another individual is committing or attempting to commit a burglary of such dwelling [or occupied building], may use deadly physical force upon that individual when he or she reasonably believes such to be necessary to prevent or terminate the commission or attempted commission of such burglary….
A person commits BURGLARY when that person knowingly enters or remains unlawfully in a dwelling [or occupied building] with the intent to commit a crime therein.
Note that building includes "any structure, vehicle or watercraft used for overnight lodging of persons, or used by persons for carrying on business therein," and there's also a similar instruction as to deadly force to prevent arson, which is not limited to burning of occupied buildings.
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This, of course, is just the tip of the iceberg: There are various limitation to these rules (e.g., if you're actually the initial aggressor, or if you know there's a good-faith dispute about the ownership of the property), and I'll note again that the rules and their interpretation can vary sharply from state to state. But this is the big picture, which I think helps show the complexity of this area of the law.