I have watched our cat climb right over a 6 foot tall chain link fence. She uses it like a ladder and climbs right over it. Funny thing is she does it to get into the chicken run and the gate to the run is open and the chickens are all out in the yard...I think she just does it to show us that she can!
Some dogs can do this. One funky looking terrier climbed my mom's 6ft run years ago and proceeded to mate with her prized and babied pekingese. Mom cried about this for days. She cried more when she found out her dog was pregnant. Then had to try to find people to take these puppies that I'm sorry to say were ghastly fugly.
Bug eyes, long legs, flat face, wiry hair that stood straight up. Looked like a creature from Star Trek.