In practice the fund rarely operates that way. It is reluctant to cut its members off, especially if they have powerful friends.
This month, for example, it approved a $6bn loan to Pakistan, which has often flouted its prescriptions in the past.
And even its biggest-ever loan, over $50bn approved for Argentina last year,
was not enough to stop capital fleeing and the peso slumping in subsequent months.
Rather than rely on the uncertain protection of the fund, many members have chosen to look after themselves,
accumulating over $11trn-worth of reserves between them.
Its next boss will find its cupboard a little bare. America is opposed to increasing members' "quotas":
their permanent financial commitments to the fund (which now come to $660bn).
Instead the IMF is trying to shore up alternative sources of financing, including $250bn it has borrowed for five years from 40 richer members.
Limited firepower also threatens its legitimacy. A country's financial contribution to the IMF determines its share of votes in the institution.
So without an overall increase in quotas,
the fund will struggle to redistribute voting power from over-represented countries in Europe to faster-growing members elsewhere.
To do so would require cutting some members' stakes in absolute terms, rather than merely freezing them as others expand.
China, according to the IMF's independent evaluation office,
is now more under-represented than it was before the voting reform of 2008,
because its share of global GDP has grown faster than its share of IMF votes.
The fund's response to this impasse has been innovative.
Just as it has sought alternative sources of financing, it has also sought alternative wells of legitimacy.
Ms Lagarde has energetically broadened its concerns to include inequality, gender and climate change.
Critics worry that the IMF is now spreading itself too thinly,
taking on new tasks when it has yet to master its customary responsibilities.
It does not seem sure how to stop prices from rising in Argentina or those in Japan from threatening to fall.
Should it wage an additional crusade against rising temperatures worldwide?
But its new preoccupations may also help it meet some of its core duties.
Its traditional advice to tighten belts, for example,
carries more weight in many parts of the world because it has shown that it is sensitive to broader social ills.
Good parents know that showing the cane is no substitute for showing that you care.