In a building with gated entry, if a resident lets a stranger into the building, and he turns out to be a thief, would the resident who let him in be liable for the damages?
The primary legal question is whether the resident (tenant) has breached a duty of care. There are all sorts of laws establishing duties of care, such as between doctor and patient, which may be created by a legislature or may be part of common law tradition. There is a duty of care imposed on a landlord w.r.t. the tenant, requiring that the premise be "secure", therefore a landlord might easily be held liable if the main door into the building was not locked. This duty is a specific instance of a general duty from tradesman/businessman to customer.
As far as I can determine, there is no such statutory duty imposed on tenants in Washington state, and none from case law being revealed by a few cursory searches. In order to be subsumed under general "everybody has a duty to everybody else" law, the damage would have to be foreseeable. It is said that "If something is foreseeable, it is a probable and predictable consequence of the defendant’s negligent actions or inaction". This mean that a reasonable person would have known that, under the circumstances, the damage is likely to result. Circumstances vary quite a bit, and there is no general rule about holding the door open for another person. If there is abundant signage reminding tenants to never ever let in a stranger no matter that their excuse and/or if the premise is in a crime war-zone, the outcome is more likely to be considered to be foreseeable.