Yes, you can be liable if an unauthorized person trespasses on your property. Fortunately (and unfortunately), every situation is different. Generally, as the owner of a property, you aren’t responsible if a strange person comes onto your turf. You may get a judge that disagrees that you should be liable, depending on the case, and the general rules that say otherwise. What the liability really has to do with, is whether or not you have been aware of the hazard, have knowingly had a few trespassers, and have done nothing about it. By definition, a trespasser is a stranger that enters onto a property when they were not given permission by the owner to do so. You will likely be responsible for their injuries if:
1) the hazard is one that the owner created him or herself, and/or maintained themselves
2) the hazard is likely to be fatal, or inflict serious physical harm
3) that the owner had strong reason to believe that trespassers would not find it
If people trespassing on a property has become a common occurrence, the owner by now realizes that this is an ongoing situation. This is when the situation starts to get tricky. If the same issue is continuing to happen (trespassers continually coming onto the property and getting hurt), the owner by now realizes that they need to either remove or fix the hazard, OR make a large sign informing them that there is a hazard ahead (such as a deep pit in the yard for example).If you are a property owner, it is your right to defend yourself against an armed robber or murderer. If someone breaks in and you shoot them, you are legally protected and justified.
An entirely different set of rules applies when minors are involved. Property owners have a responsibility to make sure that their property is safe if children are entering the property. For example, if you have a pool in your back yard but no fence. It is simple for a child to wander into the yard and fall into the pool, or hit their head when trying to do a pool trick.
A property owner has a responsibility to inspect and monitor their property to see if there are any unsafe conditions that might attract children. If there are, the owner must fix them as soon as can be done.
A property owner can be held responsible for an injury to a trespassing child if they know that children were likely to trespass, or they were not aware of the risk.