Yes, if a domestic cat was unfortunate enough to meet a tiger who was looking for food it is likely that the tiger would kill and eat it quickly. A small prey item for a tiger.
There is no mythical ‘feline agreement’ between all the species of cat which says that they should never kill and eat each other.
Tigers eat almost anything that they can catch. Highly opportunistic. They’ll eat frogs and elephants and everything in between including other carnivores.
My source tells me that there are records of ‘tigers killing…bears, leopards, lynx, wolves and foxes’. The leopard and lynx are cats. The former is large and the latter is medium-sized. Leopards avoid tigers.
I would doubt that there is a formal record of tigers eating domestic cats because it is not significant or notable. But if there are records of tigers eating leopards it is impossible to argue that they won’t eat domestic cats.
They are food like any other animal. Almost any terrestrial vertebrate is a potential meal for the tiger. They often take large prey including domestic animals such as domestic buffalo and cows.
Deer are perhaps the common prey of the tiger but the odd domestic cat wandering around the perimeter of a remote village in India near a tiger reserve might disappear from time to time and no one remarks on it. Domestic dogs are equally at risk I suspect.
P.S. Tigers even eat fish.
The source is page 349 of Wild Cats of the World by the Sunquists, the best book on the wild cats bar none. There is one issue with the book now: it was published in 2002 and the conervation of the species deteriorates yearly due to the relentless pressure from human population growth notably in the countries where the tiger is found.
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