Analysis: Daniel Gallas, South America business reporter
Not very long ago, Petrobras was living one of the most exciting moments in its 61-year history.
In 2007, the company discovered massive oil fields about 5km beneath the seabed off the coast of Brazil.
The then President Luiz Inacio Lula da Silva even joked that this was proof that "God was Brazilian".
But much of that lustre has come off since last year, when a major corruption scandal was unveiled, including allegations that some executives were channelling 3% of the proceeds of major contracts straight to politicians' campaign funds or pockets.
Petrobras is also facing financial challenges too. Low global oil prices have hurt the company's long-term investment plan.
Also, as part of the Brazilian government's efforts to hold down inflation, the company has been subsidising petrol. That has helped consumers' budgets, but it has damaged Petrobras financially.
Rebuilding Petrobras' finances and reputation is the main challenge faced by whoever is appointed by President Dilma Rousseff.
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The illegal activity, the authorities allege, diverted anything from $3.7bn to over $28bn from Petrobras assets.
Ms Foster has said publicly that she offered to resign when the corruption scandal broke, but maintains she did nothing wrong.
The scandal has also damaged President Rousseff, a former chairwoman of the company's board of directors. She has denied any knowledge of corruption.