There are two major classifications of crust on earth: oceanic and continental. Oceanic crust (mostly basalt/gabro) is quite a bit more dense and thin than continental crust (mostly granite). Both float on the more dense mantle like big rafts, but the much thinner and denser oceanic crust sits ~3 km lower on average, creating ocean basins. In fact, the cold oceanic crust (and its attached subcrustal lithosphere) is in some places more dense than warmer mantle at depth; this density contrast is part of the convection cells in the mantle that drive plate tectonics.
When an oceanic tectonic plate converges with a continental plate, the denser oceanic plate slides underneath, at a subduction zone. (edit: I tried some ascii art to illustrate but HN deleted the spaces and ruined it; I fixed it in a comment below.)
There are three types of earthquakes that happen in oceanic plates in subduction zone environments. The first, most familiar and strongest are subduction zone or 'megathrust' earthquakes, like Tohoku (Japan 2011). This is an earthquake caused by the release of stored energy due to frictional locking between the downgoing oceanic plate and the upper continental plate.
The second type is an 'outer rise' event. These are almost always small (M~6 max) and not very damaging. This is caused by the flexing of the oceanic plate as it gets ready to dive down (@stephengillie, this is the stress you're asking about).
These types of earthquakes are easily observed because they're shallow and relatively well understood.
The third type of earthquake is what the Mexican event was; it's an earthquake that happens within the subducting (downgoing) slab/plate at depth (see diagram in comment below). It's not clear exactly why these happen but the pattern of energy release is consistent with vertical(ish) contraction and horizontal(ish) extension, i.e. normal faulting. The best explanation for why a downgoing slab would be contracting vertically and extending horizontally is that it is slowing down as it descends, probably due to a decreasing density contrast between the cold (but warming) slab and the mantle around it. So basically the downgoing slab is buckling like a train would if the front train cars slammed on the brakes but not the back train cars. Actually the best way to visualize this is to think about dropping a flexible rubber sheet (that is more dense than water) into a pool. It will continue to sink in the pool but more slowly than in the air above, and will buckle at the interface due to the buoyancy contrast.
But (unlike at the surface) we can't directly test this hypothesis because we don't really have any data on the velocity field to see if there is a deceleration of the downgoing slab (plate). Many of these deep intraslab events, particularly at 100-700 km depth, are thought to be associated with density changes in the downgoing slab as it undergoes mineralogical transformations to thermodynamically restabilize in vastly different P-T conditions.