A classical example of the limits of static equilibrium is an object
acted on by gravity and a normal force from a horizontal surface.
If we consider a brick standing on the table then the normal force
cancels the force of gravity and if it is a simple square brick then
none of these forces exhibits a finite torque about the center of mass
point. The brick is therefore can remain in static equilibrium. If I push the top of the brick I can maintain the
brick in static equilibrium in a tilted position. To analyze
static equilibrium
it is convenient to choose the point of contact with the ground as the
point of reference. Only gravity and the pushing force have torque.
As long as the center of mass point is on the side of the
reference point where the brick is being pushed it supplies
a torque opposite that of the pushing force and hence a static
equilibrium is possible. When the center of mass
point lies exactly above the contact point we have an
unstable static equilibrium. As soon as the center of mass point
moves beyond the point of support
the brick falls since now the pushing force produces a torque
of the same sign as the torque from gravity and hence no static equilibrium is possible.
You must be aware of these sign changes as important markers for
different conditions of static equilibrium. Specifically forces tend to
be limited to certain directions: For example a string can only pull
a normal force can only push. Furthermore there are limits
to the magnitude of frictional forces. For example the static friction
is limited 
. If the static equilibrium conditions
require that a string should push or a floor should pull or
then there cannot be a static equilibrium because it
would require impossible directions or magnitudes for these forces.