How does the SureStop braking system work? There's a new braking system put out by a company named SureStop that controls both front and rear cantilever (side-pull) brake systems with a single brake lever.  They seem to be mainly appealing to the safety / children / new bike owner's market.

They say their technology can prevent end-overs as well as skid-outs.

How do they do this? It appears to be more complex than a dual-cable brake lever -- i.e., there seems to be some fore-aft balancing magic that's going on. 

Bonus question: If the rear pad loses traction against the wheel (for example: it wears down to its nubbins, slips off the rim, or the rear brake cable breaks), does the user lose all braking - front and rear? Does this then violate the redundant brake regulation in bicycle consumer sales laws?

For example, Japan's JIS 9301:2010 regulations requires "separate braking systems operating on the front and rear wheels respectively" and SureStop says that they are compliant with this standard. Because the front and rear brakes are linked in SureStop, it's unclear to me how they are "separate."
You've got a brake lever and a rear brake both with typical mechanical advantage characteristics. One of the rear pads has a spring-loaded sliding mechanism where forward momentum captured from the back wheel when braking causes it to slide forward and actuate a cable going to the front brake, which is controlled only in this manner. (The head of the cable is in the moving pad, and the stop for its housing is a stationary part of the pad. Movement between the two generates the cable movement, same as a brake lever.) Some assumptions are built-in about weight distribution and total weight on the bike, and the manufacturer chose a distance for the slidey bit that will keep the front brake from ever being able to lock if those assumptions are correct.

Maximum braking power is decreased compared to a normal system owing to the aforementioned one-size-fits-all design assumptions, which have to be conservative for the system to do its thing, which in the scheme of things probably makes them less safe for most people, not more. They are adequately powerful for most purposes when set up correctly. Their marketing/product material touts the line that they're a pure, unequivocal upgrade over conventional systems, which is not correct because they reduce the overall amount of braking power available.

Another safety drawback, especially for novice or fearful users that might be most drawn to the system, is that not adjusting the rear brake's barrel adjuster as the rear pads wear will create a situation where the entire bike has inadequate or no brakes much faster than in a conventional two-lever setup. For a rider that simply will never use their barrel adjusters, SureStop is much more dangerous. Compounding the issue is that the front brake has its own adjuster, but using it properly is a little more complex than normal (see their videos for more explanation.)

Another way of looking at how it works and the effect on power is that you've got a normal rear brake you can set up and use however you want, and for your front brake someone put an arbitrarily sized block of material between the lever and the bar so the lever will always bottom out against it at a certain point in its travel.

Any loss of grip between the rear pads and rim, or any mechanical failure of the rear brake, will keep the front brake from operating, rendering the bike brakeless. In other words, the system eliminates one of the key safety features of other bikes with two brakes: redundancy in case of mechanical issues, especially in emergency braking situations where cable systems in particular are stressed the most. 

A theoretical advantage of this kind of system is for one-handed users, especially if the one braking hand available has compromised strength. Unlike split levers, they don't have the drawback that they're dividing one hand's braking force between two different brakes, since they're making use of otherwise-wasted energy to actuate the front brake.