An example of domesticated animal that became invasive species?

Cats are an example.

Here are a few examples of released pets becoming problematic in the United States:

Lionfish: Originally from the Indo-Pacific, these venomous fish are wreaking havoc on native fish populations in the Western Atlantic, Caribbean, and Gulf of Mexico. Considered the “Hoover vacuums of the sea”, lionfish will eat anything up to half their size. Despite being highly invasive, they are still imported in the States in large numbers: 46,000 lionfish were imported in 2011 alone.

Cats: Your cuddly kittens have a deadly side. Domestic outdoor and feral cats kill a median of 2.4 billion birds and 12.3 billion mammals every year, leading cats to be considered one of the largest human-linked threats to wildlife in the country.

Giant African Land Snail: These massive mollusks are one of the word’s largest snails and consume more than 500 types of plants. To top it off, they can damage plaster and stucco structures and can carry a parasitic nematode that causes meningitis in humans.

Burmese python:  Reaching up to 17 ft in length, Burmese pythons are some of the largest snakes in the world. Now established throughout South Florida, Burmese pythons pose a serious risk to native wildlife and domestic pets. More than 2,000 pythons have been removed from the Everglades National Park since 2002, a figure that likely represents a small fraction of the population.