Sorry, was going to do this all as one post but I forgot we can't edit in this thread.
With a helmet, it will come to a less sudden stop and thus reduce the chances of brain injury.
That is the theory. The practice is different. There are 3 matters to consider:
1) Cycle helmets are only designed to protect against impacts up to 12MPH. It is unlikely impacts at sub 12MPH velocities would cause brain impact injury or structural skull injuries anyway.
2) If this is the case, why is there no reduction in death by and serious head injuries among cyclists in countries and states where compulsory wearing has been introduced? The correlation is the opposite - the countries with some of the lowest rates of this type of death and injury among cyclists also have some of the lowest helmet wearing rates.
3) Motorcycle helmets work by a difference mechanism. The hard outer shell spreads the mechanical load, and thus gives a genuine and useful reduction and progression or deceleration as that also spreads the area of internal deformation. Cycle helmets give only a localised deformation, and do not reduce the deceleration curve in any where the same manner. Squeeze 1 inch cube of polystyrene in your fingers and you'll feel it give easily - now squeeze a 6 inch square that is 1 inch thick and you'll feel the energy required to deform is much greater. They also provide zero penetrating and virtually no direct trauma protection as they lack the outer hard shell of motorcycle helmets. Because they also lack the hard, featureless, slippery outer shell it has been discovered that they can cause rotational brain injury and torsional spinal injuries, injuries that can themselves be fatal, yet a couple of years ago before this was discovered you were still preaching that helmets save lives. MIPS mitigates this somewhat, but does not eliminate it, particularly the tortional spinal injury, but the majority of helmets do not have this type of construction anyway, yet still you blindly claim helmets will save us.
People thoughtlesly believe cycle helmets save lives. Well, they surely must, right? They're helmets, safety devices after all. OK, then show us the clear and reproduceable evidence of this instead of make claims that are not founded on actual evidence. There have been some fantastic, ultra large scale real life experiments out there with entire countries that have made helmet wearing compulsory, populations of tens of millions, yet you have failed to explain why they are universally seeing no reduction in death or serious injury among cyclists in these countries if the helmets they are now forced to wear are the life savers you claim, despite the much lower number of cyclists that the legislation universally leads to.
In fact, the reduced cycling numbers of cyclists in these countries is very relevant to the helmet issue, as death through physical inactivity is many times more likely than death by cycling. Hell, death by walking is more likely than death by cycling.