No. Even with incomplete repairs, a tenant must continue paying rent on time and in full. If a tenant stops paying rent, they can face eviction.
If a tenant moves out during repairs, the tenant can talk to the landlord about reducing rent for this period. The tenant may want to talk to the landlord about extra costs (e.g., accommodation, eating out) of moving out. If the landlord agrees to reduce the rent or pay for any of the tenant’s expenses, the landlord and tenant should get the agreement in writing and sign it. Without such an agreement, the tenant should keep paying rent in full.
If the landlord will not voluntarily agree to reduce the rent and the tenant thinks that the landlord has interfered with their right to enjoy living in the property, then the tenant could apply for a rent abatement in Alberta Court of Justice Civil or through the Residential Tenancy Dispute Resolution Service.
If a disaster (e.g., fire, flood) completely destroys the property, it is likely the lease is frustrated. This means the lease is unable to continue and the agreement will be over. But if premises are repairable, it is likely the lease will be able to continue.