If there are budget cuts, one area that is likely to continue to thrive is the enforcement of the Foreign Corrupt Practices Act, which prohibits paying bribes to foreign officials to win business in their countries. The Justice Department depends in large part on companies to self-report violations of this law and conduct internal investigations to determine the scope of the misconduct.

The roots of the government’s crackdown on overseas corruption can be traced to the administration of George W. Bush, and it was continued aggressively by President Obama. Many of the cases involve foreign companies that have paid millions of dollars in fines, and they are a way to show the public that global enterprises are being overseen to ensure compliance with American law.

One domestic corporation likely to resolve a case under the new administration is Walmart, which has already spent more than $600 million to investigate bribe payments in its foreign operations after reporting by The New York Times revealed questionable conduct in 2012. The giant retailer was reported to have rejected an offer from the Justice Department to pay a $600 million penalty, but that opening gambit signals that the investigation is nearing a settlement that Mr. Trump’s new attorney general can announce.

The benefit of how the foreign bribery cases are pursued is that the cost is borne by the private sector. Although prosecutors proclaim they do not necessarily accept the findings of the law firms hired to ferret out misconduct inside a company, there have been few cases in which the government committed significant resources to investigate on its own. It is unlikely that Mr. Trump would want to be seen as going soft on corruption after some of his rhetoric during the campaign, so the Foreign Corrupt Practices Act is likely to remain a featured player in white-collar enforcement.

The S.E.C. in the cross hairs

The Securities and Exchange Commission has become a punching bag on Capitol Hill, with regular efforts to cut its budget and restrict its rule-making authority. President Obama was able to fend off most of that, but with the House and Senate still in Republican control, and a Republican administration, there is a chance that significant changes will be imposed on the agency.

Any reduction in its appropriations will hit the S.E.C.’s enforcement program, which has reported annual increases in the number of fillings each year under its chairwoman, Mary Jo White. Those statistics were padded a bit by cases for minor violations, a reflection of Ms. White’s “broken windows” approach that emphasizes enforcement for small transgressions in the hope that it will prevent large problems. Interestingly, Mr. Giuliani pushed that same policy to reduce crime when he was mayor of New York.

Of greater concern for the S.E.C. may be a change in its authority to pursue cases in administrative hearings outside of federal court. The Dodd-Frank Act gave the agency the authority to obtain penalties against any defendant in these proceedings, so it had the choice of where to file an action. An administrative case can be pursued more quickly because the rules do not allow for broad discovery of evidence by a defendant, and the initial ruling is decided by an internal judge working on a tight deadline, not by a jury.