Negative Gini Coefficiente? Is it possible to have a negative gini coefficient?
In which situations is it possible?

Any help would be appreciated.
tl;dr No, it is not possible to have a negative Gini coefficient.

The Gini coefficient is the area between the line of equality and the Lorentz curve, and this area cannot be negative. Let the area of equality as in the link be denoted by $A$, and the area under the Lorentz curve be denoted by $B$, then the Gini coefficient is given by

$$ G = \frac{A-B}{B}$$

If negative income (or whatever you are measuring) is not permitted, the maximum inequality is $1$. If negative income is permitted, it can potentially be larger than $1$. In any case, the minimum for the Gini coefficient is $0$, which corresponds to total equality.