With regard to ATP synthesis, as electrons flow down the electron transport chain, the protein complexes are pumping protons across a membrane creating a proton gradient (a greater concentration of protons on one side of the membrane than the other). As a result, there is a driving force to drive the protons back to the other side until both sides have the same concentration of protons (in other words, it's diffusion). The way that the protons make it across is through a protein known as the ATP synthase. It allows them back to the original side and uses the energy of the protons diffusing down their concentration gradient to synthesize ATP.
In short, the electron transport chain backs up because there's nowhere for the electrons to go--however, there's still a proton gradient that will drive protons to flow through the ATP synthase (which isn't part of the electron transport chain--it just happens to be in the same membrane). As a result, ATP synthesis will continue until the existing concentration gradient runs out. Normally, electrons would continually flow down the electron transport chain continually pumping protons to maintain the gradient...but with no more electron transport, no more proton pumping occurs and the gradient vanishes as the proton concentration is allowed to reach equilibrium on both sides of the membrane.