In stable resonator the beam move inside the cavity many times repeatedly.
An unstable resonator is a design which enable the beam a small number of passes through the optical cavity before exiting it.
An example of unstable resonator is the convex - concave optical cavity.
Such optical cavity is made of one big convex mirror, and one small concave mirror, and they have a common center of curvature (as seen in figure 8.2).

The beam exit the optical cavity around the edges of the small concave mirror.
The shape of the beam is the same as TEM00 mode, but with a hole in the middle.
This resonator is used in continuous wave high power CO2 lasers.