All that the sign does is clarify that the trespasser is indeed a trespasser, and that they can’t rely on an impression of consent to be on the property. It’s not all that significant.
If the property is a nuclear reactor, or an enclosure containing dangerous animals, obviously the owner isn’t liable to the trespasser. The hazard that befell the trespasser came about as a result of a lawful exercise of the property, the owner being under no legal duty to trespassers to limit the ways in which he may use his property.
The same would likely apply to security mechanisms specifically designed to deter break-ins, such as dangerous guard dogs, an electric fence, or some similar automated system that could inflict harm on trespassers.
HOWEVER, there is a distinction between this, and a situation in which the owner sets up traps to capture trespassers alive, say, and then does all sorts of perverted and terrible things to them - that Eugene could no doubt dream up - on the grounds that they were trespassing, and therefore he can do whatever he wants to them.
The distinction is that in the former instances, the owner never uses force against the trespasser - either as an unlawful initiation of force or a lawful response to force. The harm that befalls the trespasser results from a lawful utilisation of the property by the owner together with the unlawful ingress by the trespasser, therefore the trespasser bares the cost of his actions. In the latter situation, there is a proactive use of force by the owner in response to the trespasser’s unlawful ingress against his property. A response to an initiation of force must be reasonably proportional.
Trespass, if that’s all it is, is not a terribly serious crime in itself. I would contend that it is only prima facie legitimate to use force in response to trespass to the extent that it is reasonably gauged to compel the trespasser to vacate the unlawfully occupied property post haste.
Likewise, regarding theft, retaliatory force is only prima facie appropriate inasmuch as it is reasonably gauged to compel the thief to return what was stolen. Why not kick thieves out of the city?