Without a lease or rental agreement in writing there is little the property owner can do.
Personally, my response at the next renewal would be something like "I will continue to be unreasonable while you get used to being homeless", or perhaps a 100% increase in rent with a stiff damage deposit.
Re: above comments about insurance policies; I did thousands of property inspections for insurance companies over several years. Every major insurance company of which I am aware WILL DECLINE a policy, or REFUSE TO RENEW a policy, if they find that there is a dog of several different breeds kept on the property (either by the owner or by a tenant). I once inspected the same house for 4 different insurance companies, and every time I showed up the same 4 American Staffordshire Terriers (pit bulls) were in the yard and behaving aggressively, easy to photograph and document for the underwriters.
Insurance policies are contracts providing specific coverages in exchange for payment of premiums and owner's agreement to abide by contract provisions during a specific policy period. Coverage exclusions are common, specific dog breeds are frequently mentioned, and any dog displaying aggressive behavior may be grounds for declining to issue a policy, for terminating an existing policy, or renewing an existing policy. When such specific exclusions exist all risk of loss passes directly to the property owner.
Edit: One more quick thought; For those who have mortgage loans on their properties, should you ever find yourself without a current property insurance policy the bank or mortgage company might just invoke their contractual rights to call the loan due and payable immediately.
I doubt that 3 people in 100 have ever read their insurance policies or mortgage contracts from start to finish, but there are a whole bunch of terms, conditions, and remedies spelled out in detail.
