I worked with racing greyhounds for many years, they are definitely not small dog or cat safe outside, because chasing, quick of the mark, and fast is what they do.
Indoors, mainly couch potatoes. For a time I worked for a wonderful, eccentric English lady, who took all her ex racers home to retire. Best job ever, she had a manor house, acres of land and up to 12 dogs, both indoors and out, it was a hoot.