No, a country cannot have a negative GDP. The growth of GDP in a given year or quarter can be negative (as happens during a recession) but the GDP as a whole cannot be negative.
The reason for this is that GDP is a measure of the market value of all final goods and services produced in the country in the given time period. When you think about it, this cannot be negative. A country cannot produce a negative amount of goods. In addition, the value of goods produced cannot be negative.
So a country cannot have a negative GDP because GDP measures the market value of products and that cannot be negative.
The Gross Domestic Product or GDP of a country is a way of expressing the measure of all the economic activity that takes place in a country. It is the market value of all the products and services that are created within the borders of the country. There are many ways of calculating the GDP.
The GDP of a country cannot have a negative value as it is impossible that all the goods and services created in the country are sold for a negative value (something that implies that the producers actually pay the customers for everything that the customers buy.)
As used in economics GDP is an abbreviation of the term Gross Domestic Product. It refers to the total goods and services produced by country. GDP provides the country with the basic means of subsistence such as essential food and shelter. GDP also provides additional goods and services used in raising the standard of living above the minimum subsistence level.
A zero standard of living would mean that an economy generates no food or shelter at all. In absence of these, they can not survive for long. While we can think of individuals generating no useful output, and still managing to survive on borrowed money or charity. However, if no one in the economy produces anything, there will be no one left with anything to give to other as loan or charity. For this reason each and every country in the world has a positive GDP. It is not possible for a country to survive as a country or an economy without some minimum positive GDP. Thus no country can have a negative GDP.
Negative GDP would mean that the accumulated wealth of people in the economy, for some reason, is destroyed by an amount that exceeds the net goods and services produced . We can conceive a situation of this kind on a temporary and limited scale, due to natural disasters like floods and earthquakes. But these are never widespread enough to completely wipe out the GDP of a whole country.