The nicely and carefully written question Have any animals that have been studied onboard the ISS come back alive? has an affirmative answer that applies to the space shuttle. Now that return to Earth comes in capsule form, have animals ever returned live to the surface — by design?
A nice example would be the recent splashdown of the first SpaceX Dragon capsule to have been re-used after a previous visit to the ISS.
See for example Spaceflight Now's July 3, 2017 article Dragon capsule returns home with animals and station equipment:
Items stowed for Dragon’s return included live mice from an experiment to investigate the effectiveness of a therapeutic drug to promote bone growth, combating atrophy in astronauts in space and osteoporosis patients on Earth. The mice will be euthanized and examined after landing.
below: "The Dragon spacecraft was lifted onto a boat for a trip back to port in Southern California following Monday’s predawn splashdown. Credit: SpaceX" From here.
Rodent research is a big science objective for NASA. NASA and JAXA send rodents via Dragon and Cygnus capsules very frequently, and they are returned to Earth via Dragon re-entry.
The topic of study on this mission was bone tissue loss – a challenge for the health of astronauts, as well as for people on Earth suffering from osteoporosis. For the experiment, a group of mice was launched to the space station in June 2017. Half of them returned to Earth one month later, while the other half remained in space for a full two months. This allowed the researchers – a team based at University of California, Los Angeles – to study the effects of a potential treatment for bone loss, and how the body readapts to Earth conditions after an extended stay in microgravity.