Can we produce more negative voltage from a less negative voltage source? (say -8 volts from -3 volts supply)
Think about the positive voltage scenario - you can convert a more positive voltage to a less positive voltage using a voltage divider and the same applies to negative voltages - the bigger negative voltage at the input becomes a smaller negative voltage at the output.

If you want a bigger voltage in magnitude for a smaller input voltage, then you need to use an active circuit that involves energy storage such as in a boost converter.