When a country, say Greece, adopted the Euro as its currency, what happened to the debt that was based on the Drachma? Was it converted into Euros?
Yes, upon the introduction of the euro on January 1, 1999, all debt (indeed, all nominal contracts) in participating countries was converted from national currency to euros at a legally defined conversion rate. See this press release from December 31, 1998, which states:
In accordance with Article 109l (4) of the Treaty establishing the European Community, the irrevocable conversion rates for the euro were today adopted by the EU Council, upon a proposal from the Commission of the European Communities and after consultation of the European Central Bank (ECB) for effect at 0.00 on 1 January 1999 (local time). In compliance with the legal framework for the use of the euro, the irrevocable conversion rate for the euro for each participating currency is the only rate to be used for conversion either way between the euro and the national currency unit and also for conversions between national currency units.
The euro conversion rates are the following...
For the particular case of Greece, which joined the euro on January 1, 2001 instead, the conversion rate with the drachma was apparently set at 1 euro = 340.750 drachma by this regulation in June 2000.