Assume there is no emitter resistor.
Increase in VCC will lead to increase in collector current, also base current. This may have negative effect. For example, the temperature will now increase because of higher current.. As temperature increases, Vbe of a transistor reduces further..
As Base emitter voltage drops, base current would gain further triggering rise in collector current and this will make the circuit less stable.
Adding the emitter resistor counter acts by slightly opposing the rise in collector current. Whenever there is a rise in collector current, the voltage drop across the emitter resistor increases. This voltage drop now acts as a negative feedback. Higher the drop across the resistor value, lesser will be the collector current due to lesser base current.
As VCC increases, voltage drop across emitter resistor increases and similarly when VCC falls, the voltage across emitter resistor falls enabling higher collector current due to increase in base current.
Ideally I would use resistor divide bias at this base side..and keep base current only a fraction of current flowing through to bias resistors.