Refuse to Pay Government Debt Incurred for Unlawful and Oppressive Purposes,... It Is the Personal Debt of Those Who Ordered It to Be Incurred

These "odious debts" are considered to be the personal debts of the tyrants who incurred them, rather than the country's debt.

Wikipedia gives a good overview of the principle:

In
international law, odious debt is a legal theory which holds that the
national debt incurred by a regime for purposes that do not serve the
best interests of the nation, such as wars of aggression, should not be
enforceable. Such debts are thus considered by this doctrine to be
personal debts of the regime that incurred them and not debts of the
state. In some respects, the concept is analogous to the invalidity of
contracts signed under coercion.

The doctrine was formalized in a 1927 treatise by Alexander Nahum Sack, a
Russian émigré legal theorist, based upon 19th Century precedents
including Mexico's repudiation of debts incurred by Emperor
Maximilian's regime, and the denial by the United States of Cuban
liability for debts incurred by the Spanish colonial regime. According
to Sack:

When
a despotic regime contracts a debt, not for the needs or in the
interests of the state, but rather to strengthen itself, to suppress a
popular insurrection, etc, this debt is odious for the people of the
entire state. This debt does not bind the nation; it is a debt of the
regime, a personal debt contracted by the ruler, and consequently it
falls with the demise of the regime. The reason why these odious debts
cannot attach to the territory of the state is that they do not fulfil
one of the conditions determining the lawfulness of State debts, namely
that State debts must be incurred, and the proceeds used, for the needs
and in the interests of the State. Odious debts, contracted and
utilised for purposes which, to the lenders' knowledge, are contrary to
the needs and the interests of the nation, are not binding on the
nation – when it succeeds in overthrowing the government that
contracted them – unless the debt is within the limits of real
advantages that these debts might have afforded. The lenders have
committed a hostile act against the people, they cannot expect a nation
which has freed itself of a despotic regime to assume these odious
debts, which are the personal debts of the ruler.

Patricia
Adams, executive director of Probe International (an environmental and
public policy advocacy organisation in Canada), and author of Odious
Debts: Loose Lending, Corruption, and the Third World's Environmental
Legacy, has stated that:

by giving creditors an incentive to lend only for purposes that are transparent
and of public benefit, future tyrants will lose their ability to
finance their armies, and thus the war on terror and the cause of world
peace will be better served.

A recent article by economists Seema Jayachandran and Michael Kremer
has renewed interest in this topic. They propose that the idea can be
used to create a new type of economic sanction to block further
borrowing by dictators.

Odious debt is an established legal principle. Legally, debt is to be
considered odious if the government used the money for personal
purposes or to oppress the people. Moreover, in cases where borrowed
money was used in ways contrary to the people’s interest, with the
knowledge of the creditors, the
creditors may be said to have committed a hostile act against the
people. Creditors cannot legitimately expect repayment of such debts.

The United States set the first precedent of odious debt when it seized
control of Cuba from Spain. Spain insisted that Cuba repay the loans
made to them by Spain. The U.S. repudiated (refused to pay) that debt,
arguing that the debt was imposed on Cuba by force of arms and served
Spain’s interest rather than Cuba’s, and that the debt therefore ought
not be repaid. This precedent was upheld by international law in Great Britain v. Costa Rica
(1923) when money was put to use for illegitimate purposes with full
knowledge of the lending institution; the resulting debt was annulled.