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I am sorry to hear about this situation. Unfortunately, no - in most circumstances the landlord would not be negligent.
Well this is because the landlord owe no duty to intervene on behalf of a tenant or to make sure that a tenant is not harassed/injured by another tenant. This is simply outside their purview.
In fact, the elements of negligence are: duty of care, breach of that duty, and damages. The landlord has no duty of care here. They are not responsible for a tenant's actions unto another tenant.
However, of course one still has recourse against the neighbor and their cousins, both civil and criminal. If you tell me what state this is in, I can be more specific as to what kind of recourse one has.
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