How emitter resistor provide more stabilization?

The emitter resistor places limits on the required gain, and temperature stabilizes the transistor. Without it, gain is hFe, but that is variable, temperature dependent, and subject to thermal runaway. With it, gain is predictable (collector resistor divided by emitter resistor, though limited by hFe), and temperature stabilized (so long as both resistors have the same temperature coefficient, and so long as the hFe margin is maintained).