If a tenant is suffering from harassment (continual) from the other occupant in their building ( with police reports) and the management continually says it's your word against theirs, can the tenant break the lease without penalty?

Start carrying a digital record in you pocket, when you enter the building turn it on, each day, play the recording to the landlord, if he fails to protect you give notice to him of the violation and file charges.

If there is proof, ( but if there was proof the police would have arrested them? ) without proof it is just your word against thiers and the landlord can not do anything.

And if you move out, the judge will say fine, just show the proof ?