Speaking in physical terms, even quantum mechanical physical terms, an electron density of zero means that an electron would never, ever be at such a location (zero probability). A negative value would have no meaning.
Speaking mathematically, this result derives from electron density for a single electron being the square of a value and even a negative number, when squared, will be positive.
What your diagram is showing is that in a carbon dioxide molecule the carbon nucleus is electrophilic. Because of the orbital configurations, the electron density around the carbon nucleus is low, relative to the 6 protons in the carbon nucleus, but the density is not negative (nor even zero). The greedy oxygen nuclei keep the electrons hanging out closer to them (conceptually). This is all a product of the molecule's orbital configurations.
As described by Mr Mabey, electron density around c in co2 will never be nagative. It is useful to mention the concept of dipole moments which gives the probability of finding electrons around c in co2 is much less than that of o. So it is clear that electron density around c is less than o and a temporary negative and positive pole is formed between o and c. Although the electron density around c is positive it would be the negative part because of relative electron congestion around o.