Yes, There Is Such A Thing: Federal Employee Unions, Paid For By Taxpayers
Paid for into the billions of dollars. And just to be clear, they aren't doing government work; they're working for the unions that represent federal employees.

Jeff Bergner, at The Weekly Standard, calls for the elimination of taxpayer funding for these unions, and I'm right behind him, cheering that:

These unions, opposed by Franklin Roosevelt, George Meany, and others of consequence, were first authorized by executive order in the Kennedy administration. These unions have become deeply institutionalized and built into a web of civil service laws. As a matter of general principle, the only people who should sit across the bargaining table from union leaders are people who are putting up their own, and not taxpayers' money. Moreover, there is at this time no demonstrable need for federal government unions when federal salaries and benefits far exceed those of the average American worker. Eliminating federal employee unions, however, would be a very heavy political lift.

A less radical, but still very significant step would be to terminate taxpayer funding for federal union representation work. For example--as unbelievable as it sounds-- more than 200 federal employees of the National Treasury Employees Union are paid government salaries--many in excess of $100,000--to do union work. In a perfectly Orwellian formulation, this union work is called "official time." The cost of this taxpayer-subsidized union work, which amounted to 573,319 hours in 2013, was $23.5 million.

Overall, it is estimated that federal government union officials each year expend more than 2.9 million hours, at a cost to taxpayers of $121 million, on "official time." Surely these positions could be defunded. Union members could support their leaders, if they choose to do so, out of freely collected union dues.