Suppose you have metallic solids inside an indestructible tube, with a very powerful and indestructible piston - the piston gets a tiny hole on the piston.
What would happen if you compress the solid inside really really hard? (say, $10^{14}$ Pa)
Will the metal "runs" out from the hole? If so what kind of state will the "escaped" metal be during the whole process? liquid? Solid?
Strength is relative
If the hole is made in the piston first and then pressure is applied gradually, it would resemble this:
In this image as well as your example, the tube and "piston" are much stronger than the material being compressed. For strong materials being compressed, your piston would be held together forces that far exceed the theoretical maximum strength of any chemical bond.
Not a perfect analogy
A more brittle metal would likely fracture and come out as a bunch of particles. That being said, heated aluminum can be extruded like toothpaste. This process can even fuse parts of the metal together, which allows making complex shapes with holes. Most "strong" materials would probably come out hot to the touch.
Extreme conditions
The previous discussion assumed that the pressure is applied gradually after a hole is introduced, in which case any material would be extruded/fractured out of the hole long before $10^{14} Pa$ was reached. However, if $10^{14}\text{ Pa}$ is applied first and then a hole is opened the picture is much more violent. At these pressures most of the pressure would come from electron degeneracy pressure. According to this paper ($10\text{ erg/cm}^{3} = 1\text{ Pa}$) a material like carbon is compressed to about $30\text{ g/cm}^3$ at $10^{14}\text{Pa}$ (diamond is only $3.51\text{ g/cm}^3$ at atmospheric pressure). This stores about $1000\text{ kJ/g}$ of elastic energy! TNT is only $4\text{ kJ/g}$. It would come out as a jet of plasma that would destroy anything in it's path. Stand back!
