If you copy/paste the laws and post the actual situational facts, I'm sure there would be some legal opinions given.

If the animals are left in the landlord's possession, they are not abandoned. If they are left in a dwelling without any care arranged or intention to claim them in a reasonable time, then they would be a case of abandonment.

But the owner merely has to state that they verbally told someone to care for them until *time* that they would pick them up. Then it's a case of leaving your animals in the care of someone else. That's no more illegal than boarding your dog while you go out of town.

If all you have is vague "they didn't come get their dog", then you would have nothing to give any authority. If a tenant left, and left behind animals, past the time their lease was up, without arranging with the landlord a later pick up or care, the landlord could call animal control(or the police depending on the local authority) to place a complaint of abadonment and have the animals taken by animal control(or the police, again, depending on area).

This is all of course, vague since there's no details or facts given and based on my own local laws, since i don't know the area laws or the area you're speaking of.