PNP transistor in cc mode
Firstly, understand that there is no such thing as absolute  negative voltage. Voltages are always relative. Negative Voltage means that this voltage is negative with respect to some reference voltage. Most of the times that reference is ground potential. So you are correct when you say, that base potential must be negative with respect to the Emitter Potential. For example, to turn the transistor ON (usually saturation mode), the base can be at +1V  and the Emitter can be at +1.7 V.  Hence it is the potential difference that matters. Ve-Vb should be +0.7V, no matter what their individual polarities are. 

Edit: The condition for Saturation also requires that the base current reaches a certain threshold value, additional to the 0.7V potential difference condition.