Basically, you plot the cumulative income of the population from poorest to richest. If everyone had the same income, this would be a straight line from (0,0) (no people, no income) to (1,1) (all the people, all the income) because each person adds the same income to the total. If all the income belonged to just 1 person, it would be a flat line at the bottom followed by a vertical line. The Gini index compares the area under the graph with these two versions, which are an index of 0 and 1 respectively.
With negative wealth, the area under part of the graph is negative, and so that can drive it beyond the value of 1.
(Yes, total wealth of a population could conceivably be negative, if a huge debt was ultimately owed to people outside the population (eg if it is to banks, some of it must be to foreign-owned banks, and more than the population has in assets such as property). )
Actually, thinking about it, I'm not sure how a Gini index would be calculated if the population as a whole was in debt, because the right hand end of the graph represents 'all the wealth combined', and if that's negative it would make it difficult to say what '1' on the Y axis should be. Perhaps that means that external debt shouldn't be considered.
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