But the government still can’t quite bring itself to admit the companies’ shares are worthless.

The mortgage buyers’ regulator, the Federal Housing Finance Agency, said Wednesday that it told the government-run companies to delist their shares from the New York Stock Exchange. The decision, by eliminating a liquid market for the shares, sent Fannie  and Freddie into free fall.

Fannie shares, which traded as high as $70 in 2007 before the collapse of the credit bubble, recently traded below $1 each for 30 straight days, triggering an NYSE listing review. Freddie shares have been bobbing just above $1 but would inevitably have faced delisting themselves, given the firm’s dependence on the federal dole. They will now trade over the counter.

FHFA director Edward DeMarco said delisting now “fits with the goal of a conservatorship to preserve and conserve assets.”

He has a point. The firms are still in existence purely because the government has spent tens of billions of dollars absorbing losses on bubble-era mortgages and loan guarantees the companies held.

The government has shown it wants the companies to focus on propping up the housing market, which is no small task in the wake of a massive housing bubble. Estimates of the taxpayer tab have risen as high as $1 trillion.

Yet their shares have continued to trade since their September 2008 federal takeover, an artifact of the government’s decision to just take an 80% stake in the firms while shouldering the entire burden of their operation.

The stocks have at times traded quite heavily, as the computerized traders that now account for more than half of market activity flooded into low-price shares.

Yet even with both Fannie and Freddie losing billions of dollars each quarter and facing more losses as foreclosures mount, both stocks recently had a value of more than $1 billion – suggesting shareholders stood to share in some far-off recovery.

It is extremely difficult to imagine that’s so, especially considering how widely hated the companies are in Washington. The government has suggested it views the shares as worthless by paying Fannie and Freddie executives in cash, at a time when it is demanding others in the financial industy be paid in stock.

But even in mercifully ending one aspect of  the Fannie-Freddie charade, DeMarco can’t bring himself to admit the stocks — once worth as much as $1.3 trillion — have no value.

NYSE listing rules give the firms a chance to “cure” their low prices. Other companies, notably government-backed AIG , have undertaken reverse stock splits under similar circumstances, permitting trading to continue even amid doubts about the companies’ solvency.

But DeMarco ruled out such maneuvers at Fannie and Freddie, saying that the “alternatives for putting in place such a cure do not assure maintaining the minimum price level or avoiding loss of shareholder value.”

No need to worry. The shareholder value at these companies is long gone.