What's the difference between a "dead" and "empty" state?
That ∅ in the figure is just the name of that particular state in that machine.You could name it "cpx" if you want.

The figure is an example showing conversion from NFA to DFA. The conversion algorithm builds the DFA states from subsets of NFA states.The state named ∅ indicates that this state represents a particular subset of the states of the NFA, namely the empty set.

So, the symbol is just for the viewer to understand the significance of that particular state in the machine.