Puppies and dogs from shelters can have kennel cough. Three dogs of mine have had it, and Max almost died from it at age 9 because my dog Buddy had it. My other dog Lily had it so we did not introduce her to Buddy until it was completely gone, we didn't want any of our dogs getting kennel cough again. It is a definite nightmare. Max got it real bad--he was throwing up a lot, pooping/peeing everywhere, had snot everywhere.. it was just horrible. That's one of the main reason why it isn't that great to get a dog from a shelter, even though you are giving a dog a new home and stuff, sometimes it's not worth it if the dog can die from kennel cough.
Puppies and dogs from anywhere can have anything. It's not only an animal shelter problem.
Dogs from reckless breedings can have loads of defects that can't be cured. That's why breedings shouldn't be done without the proper health testing.