If that were to happen, Is there recourse against the landlord?
I disagree with Jack's flat answer of "no" to this question. It might be possible to hold the landlord liable for this if the actions of the tenant rise to the level of being a nuisance under California law. Even then, the circumstances in which the landlord would be liable for the tenant's conduct are very limited. The general rule in California is that a landlord is not liable for the nuisances that his tenant creates after the time the lease is created unless the landlord himself either participates in the nuisance or permits (i.e. has given the tenant permission) for the nuisance to occur.
However, there are exceptions to that. One of them is where the landlord has knowledge of the nuisance and renews the lease after that knowledge. And another is where the landlord has knowledge of harm from the nuisance and has the ability to act to remedy that harm but fails to do so.
There was a case in which a neighbor alleged that the tenant's dog was running around defecating and urinating on neighboring properties and one of the claims against the landlord was founded in negligence. Assuming that the dog was creating a nuisance, the court still held for the landlord since the HOA had not proved any of the exceptions above applied. Specifically, the California appeals court said:
Assuming arguendo that evidence Kiymaz allowed the dog to run off-leash and urinate and defecate in the common areas would support an inference that the dog's behavior interfered with plaintiff's use and enjoyment of her property,6 Brown, as the landlord, would not, as a general rule, be liable for a nuisance created by his tenant after the premises are let. Generally, "a landlord is not responsible to other parties for the misconduct or injurious acts of his tenant to whom his estate has been leased for a lawful and proper **51 purpose when there is no nuisance ... at the time of the leasing." (Anderson v. Souza (1952) 38 Cal.2d 825, 831, 243 P.2d 497; see also Napolin v. Hotel Rose (1955) 137 Cal.App.2d 701, 706, 290 P.2d 925; Mundt v. Nowlin (1941) 44 Cal.App.2d 414, 415–416, 112 P.2d 782.) In Kalis v. Shattuck (1886) 69 Cal. 593, 11 P. 346, the court held: " 'To bring liability home to the owner of real property ... the nuisance must be one which is in its very essence and nature a nuisance at the time of the letting, and not something which is capable of being thereafter rendered a nuisance by the tenant.' " (Id. at p. 597, 11 P. 346.) Limited exceptions to the general rule of nonliability may hold the landlord responsible where the landlord "participated in the wrongful act by authorizing or permitting it to be done" (id. at p. 600, 11 P. 346), or where the landlord failed to conduct a reasonable inspection of the premises before renewing a lease (Burroughs v. Ben's Auto Park, Inc. (1945) 27 Cal.2d 449, 453–454, 164 P.2d 897). These long-established limitations *1374 on imposition of liability on the lessor for a nuisance created by the lessee continue to be recognized in modern cases that require, at least, a showing of the landlord's knowledge of the hazard, and ability to prevent the harm. (Resolution Trust Corp. v. Rossmoor Corp. (1995) 34 Cal.App.4th 93, 100, 40 Cal.Rptr.2d 328; see also Donchin, supra, 34 Cal.App.4th at pp. 1838–1839, 41 Cal.Rptr.2d 192; Uccello, supra, 44 Cal.App.3d at p. 514, 118 Cal.Rptr. 741.)
No triable issue of fact existed as to any exception to the general rule of nonliability. Plaintiff did not submit any evidence that Brown authorized or participated in Kiymaz's allowing the dog to run off-leash or to defecate and urinate in the public areas. The exception regarding failure to inspect was inapplicable since there was no allegation or evidence that a lease was renewed after Kiymaz created the nuisance. The final exception requires a showing of the landlord's negligence based on knowledge of the hazard, and ability to prevent the harm. Yet, for the reasons we have already stated with respect to the cause of action for premises liability and negligence, plaintiff failed to create a triable issue of fact that Brown even had knowledge of the dog's dangerous propensities or of the behavior alleged to constitute a nuisance.
Chee v. Amanda Goldt Prop. Mgmt., 143 Cal. App. 4th 1360, 1373–74, 50 Cal. Rptr. 3d 40, 50–51 (2006).
As to that last exception, I think it might be argued that the landlord once he has knowledge of a nuisance like this has the power to remedy it because California statute now has a provision in it that allows a landlord to terminate a lease with 3 days notice when the tenant is creating a nuisance. See California Code of Civil Procedure section 1161(4). I find no case law yet though in which that argument was made so I have no idea how that might turn out should you wish to try that. It'd be easier if you could prove that the landlord renewed the lease with the tenant after you had made the landlord aware of the nuisance, though. And, of course, you have to prove the tenant's actions met the definition of nuisance under California law to even have a shot there. You might want to discuss whether you may have a decent shot to win a claim against the landlord on this with a California civil litigation attorney.
Of course, if the tenant is causing a nuisance he himself is liable for harm caused by that nuisance.