Negative signs are conventions used to refer to current flow or voltage drop directions. Sometimes they represent Phase shifts.
How would you go about implementing a negative resistance? How do you eat negative bananas? The point is negative values are generally not possible physical quantities unless your dealing with theory or your bank account.
As an example take an AC generator it does not generate negative voltages just the flow has changed direction hence the negative. So as far as a negative resistance or any other negative device it is highly unlikely considering your dealing with physical quatities.
Also, what would a negative resistor, capcitor, or any other device do?
Essentially it would give energy off with out taking any energy in violating the laws of energy conservation.