Eating ground beef that has gone bad can make you sick and give you food poisoning due to the bacteria that can and will grow on the ground beef as it goes bad.
If you do eat ground beef that has gone bad you can expect to have possible vomiting, stomach aches, stomach cramps, nausea etc.
Usually the symptoms of food poisoning will go away on their own without medical treatment but still it's a good idea to see a doctor or go to urgent care if you did happen to eat some bad ground beef.
That is just to be safe and find out if you didn't get some more severe form of food poisoning.
If the ground beef feels slimy or smells bad then it should be thrown out and not eaten to avoid getting sick from it.