I've tamed a cat twice so far while playing 1.14 and both times my cat has died by walking into a hazard and staying in it until they died.

The first time it happened I told my cat to stand up which lead to it instantly running onto my campfire and staying still until it had killed itself.

The second time it happened I had my cat following me before it walked into a sweet berry bush. It then started to spin in circles, seeming to try to kill itself as fast as possible.