Stunning is not permissible, however if there is no alternative and the animal is still alive after stunning and slaughtered in a manner Shari'ah allows, i.e. taking the name of Allaah and cutting the vessels of the neck, without seperating the head from the rest of the body, then the meat of such animals is considered halaal.
The stunning usually does not kill the animal, however this possibility cannot be totally excluded, though if such an incident occurs then this would be out of the norm and is not in our knowledge and we are not required to dig into every minute bit to determine halaal and haraam. Even in an Islaamic country where the animals are slaughtered without stunning there is the odd possibility that an animal is killed in an unIslaamic manner and one may eat that meat.
What we are required is to make sure that exceptions do not become general so the Muslims should make sure that the meat they buy is from the butchers that sell unstunned halaal slaughter. In the UK, HMC claims to be such an organisation, selling meat from unstunned animals.
The matter is different for when we are invited for food. We should insha'Allaah take the name of Allaah and eat a little bit to fulfil the obligation of responding to invitation, without questioning or arguing about the source of the meat as this is not permissible for a muslim to insult his brother who invites him for a meal.
And Allah the Most Knowledgeable knows what is best and most correct.