Fig 1 shows a typical triode vacuum tube. Because of the Edison Effect, heat from the filament causes free electrons to boil off of an oxide coating on the cathode. A positive voltage on the plate attracts the electrons and the moving electrons produce a current flow. A negative bias voltage on the grid repels some of the electrons and prevents them from reaching the plate, resulting in less current flow. In this way a changing negative charge on the grid modulates the plate current.
One of the sources of non-linearity in vacuum tubes is "space charge"; electrons that leave the cathode but don't make it to the plate simply accumulate. This cloud of negatively charged electrons has the same effect as a negative voltage applied to the grid - it decreases current flow. This is often referred to as "self-biasing" and it's a non-linear term because increasing negative grid voltages block electrons, which produces more space charge, which is like making the grid even more negative, and so on.
Operating a vacuum tube at low plate voltages is sometimes called "starving" it and doesn't greatly affect the number of electrons that leave the cathode, which is primarily set by filament temperature. But at low plate voltages and currents space charge becomes an even bigger factor, just as many electrons are leaving the cathode but fewer of them are winding up at the plate, and the non-linearity which is present in all tubes is exaggerated.
In PAiA tube preamps the "Starved Tube" circuitry operates at such low voltage and current that it completely self-biases. You can see this by using a high impedance oscilloscope or voltmeter to measure the voltage at the tube grids. You will find that the grid is about a Volt negative relative to ground. All of this negative voltage is the result of electrons boiling off the cathode and clouding up around the grid.
There is more on this topic in the Design Analysis sections of any of the Assembly and Using manuals for PAiA tube preamps. You can download a zipped pdf file of the TubeHead two channel preamp here.