yes, this is a well know phenomenon. Hewlett and Packard, in their garage, made the world's purest audio oscillator at that time by making an oscillator with a filament lamp in the gain portion. As the oscillations grew, the resistance of the filament changed--lowering the gain. As the gain lowered, the natural output of the oscillator more approximated a pure sine wave.
There are crystal oscillators, and some fet oscillators, that still use this phenomenon to yield better phase noise.