Invading a country with high debt
The situation in Greece is complicated because it is part of the euro area, and NATO. It would presumably receive external aid.

But if you want a historical example, you could look at the tail end of the Depression in the 1930s. Although debt levels were not high by modern standards, governments had difficulty because of the Gold Standard. As countries moved to build up their militaries, they broke their pegs to gold. This gave them the ability to run large deficits to pay for the military spending.

Eichengreen’s “Golden Fetters” gives an overview of that era.

(The problem Greece faces that it is locked into an exchange rate system,like the Gold Standard, but it is even harder to get out of.)

In summary, the usual response is to break any existing currency pegs, default on foreign currency debt, and use deficit finance (and inflation) to handle the emergency.