Trade and economic interaction happens with countries outside of the Eurozone as well.
Paul Krugman rejects the notion that Southern European countries can emulate Germany's success because it supposedly rested on running large external surpluses, and since everyone can't run external surpluses that is impossible. While it is true that the current account balance is a zero sum game on a global scale, his analysis is wrong for other reasons.
First of all, Germany's increasing surpluses was not a cause of its relative success, instead the success is a partial explanation of the surpluses. Rational policies particularly with regard to the labor market helped make Germany more competitive, creating surpluses.
Note however that this doesn't mean that Southern Europe wouldn't benefit from reducing its reliance on foreign capital by reducing and preferably like Ireland and the Baltic states completely eliminate their current account deficit. In fact, given the external mistrust against them, that is absolutely essential. But that is different from the German situation.
Secondly, while it would be better for the people of Germany to use the products they produce domestically to a higher extent (in net terms) rather than to lend it to Southern Europeans, reducing the deficits of Southern Europe doesn't presuppose a reduction in the German surplus, or for that matter a reduction in the surplus of other euro area surplus countries like Holland and Finland. That is because trade and economic interaction happens with countries outside of the euro zone as well. Reducing or eliminating Southern European deficits can happen by reducing the surpluses of countries like for example Saudi Arabia, Singapore, China, Japan, Switzerland, Norway and Sweden (or by increasing for example the U.S., U.K. or Australian deficits).