Place the pork tenderloin in the slow cooker and season it with the salt, pepper, and rosemary.
In a small bowl, mix the balsamic vinegar, olive oil, and minced garlic. Pour the mixture over the pork.
Add the chicken broth around the pork in the slow cooker.
Cover and cook on low for 5 hours.
Add the green beans to the slow cooker during the last hour of cooking so they stay tender but not soft.
Remove the pork, slice it, and return the slices to the slow cooker to coat them in the juices before serving.