“There was some discussion about leaving alcohol and tobacco criminal enforcement in the Treasury at the time, but there wasn’t anybody who had the ability to investigate,” said Bradley A. Buckles, who served as director of the A.T.F. under Presidents Bill Clinton and George W. Bush and oversaw the transition. “Treasury wasn’t interested in building up a new criminal investigative function. I think they were happy to let it all go.”

At the heart of the proposal is cigarette smuggling, a venture that becomes more lucrative with every tax increase. Cigarette taxes vary wildly. Virginia charges $3 per carton. New York charges $43.50. A simple plot to buy cigarettes in one state and sell them in another can generate tens of thousands of dollars. Criminal organizations rely on more complicated schemes to move untaxed cigarettes in bulk, evading federal and state taxes. By some estimates, more than half of New York’s cigarettes come from the black market.

The A.T.F. once made tobacco investigations a priority, with ruinous results. The New York Times revealed last year that one major investigation spawned a multimillion-dollar slush fund for agents to tap for both business and personal expenses. An inspector general report in 2013 also found widespread mismanagement in tobacco enforcement operations. Since then, the A.T.F. has redirected all but a tiny amount of its tobacco enforcement budget to fighting violent crime.

The Trump administration has called on the A.T.F. to lead its crackdown on gun violence and criminal networks. The White House dispatched an A.T.F. task force to Chicago last summer to combat violence, and the bureau has been at the forefront of efforts to dismantle gangs like MS-13.

Alcohol and tobacco enforcement is now regarded by many agents as a backwater. “It’s a big part of the name, but a very little part of the resource expenditure,” said Mr. Buckles.

The A.T.F.’s 2018 funding request, which has still not been passed, describes an agency on the cusp of financial crisis, unable to keep up with demands and starved for critical resources. Agents are unlikely to mourn the loss of tobacco enforcement, said Michael Bouchard, a former agent and president of the A.T.F. Association, an unaffiliated group that supports current and former bureau officials.

“Violent crime is the biggest priority and always has been,” he said. “If it’s going to make it a more focused mission, then they’ll probably look at that as a plus.”