What happens when a peltier fails?
My proposed answer is as follows, based on this FAQ plus some physical realities.

The Working state is as described above, as is the Broken Connection state, but the Shorted state is not as has been presented on various over-clocking websites in most heating applications.

Firstly, it appears that peltiers often slowly decline according to the referenced article, with increased resistance and decreased heat pump capacity. 

Obviously an all-at-once failure and increase of resistance to the maximum capacity of the device can happen, but that does not mean that the heat produced by a failed 100W peltier in a heating application would be the same as if it were replaced by a 100W resistor as typically used:

Since the peltier will be installed as a heatpump, not a heater, and therefore will have a heatsink or some other ability to exchange temperature on both sides, the total heating capacity will be halved, assuming there were no other variables involved and the installation setup was the same on both the cold and hot side (same heat sink, same fan). But, in reality, since the cold-side will represent an already-colder environment and the hot-side will represent an already-hotter environment it will dissipate heat more quickly and more effectively on the cold side, at least until the two sides eventually equalized in temperature (if that ever occurred).

Therefore, my proposition is that in a typical heating application the heat produced by a perfeclty-shorted 100W peltier would be the equivalent of a 50W, poorly back-insulted, resistance element.