The phrase "rescue puppy" refers to a dog that has been saved or adopted from a difficult situation or an animal shelter where it may have been abandoned or in danger. Full definition
A number of rescued puppy mill dogs have inspired their guardians to go public with their stories and raise awareness about the abuse in such facilities. (onegreenplanet.org)
And it's our instinct to even want to rescue a puppy from a pet store or mill, but consider the risks and possible stress involved. (fourleggedguru.com)