Sometimes, I have mixed feelings when I practice karate. I was encouraged to punch hard and kick hard in a punching bag. I feel like I could break someone’s rib cage, break a arm or leg. If I get into a real street fight, I don’t think I want to kill or disable anyone.
As others have noted, death or severe injury is always a
possibility in a fight. Someone could fall and hit their head on the curb. Someone could suffer a heart attack or an aneurism. Even just holding someone down could cause positional asphyxia. This is one part of why it's a good idea to avoid fights whenever possible.
That said, these outcomes are not particularly likely in the case of an unarmed fight. For every unarmed fight which results in a lethal outcome, there are probably thousands which produce nothing worse than bruises and cut lips.
Humans are actually pretty durable. If you have never fought full-contact, you may be surprised to find that it's a lot harder to break ribs or arms or legs than you think. (Especially legs.) It can be done, but don't assume that it will be easy based on your experience hitting the heavy bag.
You should also distinguish between killing, crippling/doing permanent damage, and disabling.
In an unarmed fight, lethal results generally happen either from a fluke accident (someone falling and hitting their head on the curb) or from deliberate excessive force (repeatedly stomping on someone's head while they are down, holding a choke after someone has passed out, etc). The same applies for most other forms of permanent injury.
Disabling someone (temporarily) is what you need to be able to do in order to reliably stop an attacker. Breaking an attacker's ribs will probably slow him down and might discourage him from fighting, but won't necessarily stop him. Breaking his arm will impair his ability to fight and will likely deter him from continuing, but not necessarily. Breaking his leg will probably stop him from being able to fight, but if it doesn't it will at least prevent him from being able to chase you if you run. Note that all these injuries will heal with time and proper medical care.
Some opponents will give up after getting a bruise or a bloody nose, but you can absolutely not count on that. In order to
reliably stop someone you need to be able to
a) render them unconscious
b) cause sufficient structural damage that they are unable to fight effectively.
c) pin them so they can't move until help arrives (applicable only against a single attacker when you know backup is on the way)