In order for him to collect rent you would need to have access to the unit. As he declined your proposed modification you maintain your interest in the property until the lease expires and if he let it sit vacant then you could be liable for missed rent. However if his actions have made the unit uninhabitable you should be in the clear as he would have violated his duty to you as a tenant.
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Generally you are correct. You cannot be held liable for rent for an apartment which is not habitable.
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