NEW YORK (CNN/Money) - Shares of AOL Time Warner got off to a running start Monday, as investors reacted to news that its chairman, Steve Case, was stepping down.

But the run didn't last very long. Up more than 4 percent in pre-market trading, AOL shares finished up just 15 cents, or 1 percent, at $15.03. The muted reaction can be chalked up to the fact that everyone expected Case to go eventually.

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"It was a fait accompli," said Reed, Conner & Birdwell chief investment officer Jeff Bronchick of Case's resignation. "I just don't think it matters."

At least one investor, however, thinks the resignation, coming when it did, could signal more bad news for the troubled AOL unit, which has been struggling with weak advertising and to maintain subscriber growth as more and more Internet users move to broadband connections. (AOL Time Warner owns CNN/Money.)

Doug Kass, a hedge-fund manager with Seabreeze Partners who has a small short position in AOL, thinks that when AOL reports results on Jan. 29, the AOL unit will show a net reduction in subscribers.

"That would shake the Street," Kass said. "It will raise the specter that the division needs to be jettisoned."

Even without more bad news from the online unit, the idea of a spinoff has lately gained adherents.

"Management should be at least discussing the possibility of spinning off some of AOL to shareholders," said James McGlynn, manager of the Summit Everest fund, who is long AOL. "Normally if a division has zero value on Wall Street, spin it off, put some debt in it and see what it's worth on a standalone basis."

In fact to many investors it appears that the online unit has a negative value, because as a whole, AOL trades as a discount to other media names. But although a spinoff may come eventually, doing so now would be akin to selling a house in disrepair -- better to do some work now and get a better price later.

"How can they sell something that isn't doing well?" said Credit Suisse Asset Management managing director Stanley Nabi, who owns AOL shares. "They'll get nothing for it. I think if they can turn it around and make it solidly profitable, they'll get rid of it."

A spokesperson for AOL did not return a call seeking comment about whether or not the company is exploring an AOL spinoff.

George Gilbert, manager of the Northern Technology fund, which owns about 250,000 shares of AOL Time Warner, says a spinoff of AOL does not make sense in the short term, since the company is already in the process of readying an initial public offering of its cable unit, Time Warner Cable.

As for dropping the AOL in AOL Time Warner -- one rumor that was flying about after news of Case's resignation hit -- Gilbert thinks it would be too expensive: "Re-branding often costs a lot of money -- would that be a worthwhile use for what at this point are relatively precious assets?"

In the short term, the company should get a boost from the IPO of the cable unit. The IPO, tentatively scheduled for the second quarter of this year, could help resolve two major concerns.

First, it would give AOL Time Warner the necessary capital to complete a purchase of cable operator Comcast's stake in Time Warner Entertainment, a joint venture between AOL Time Warner and AT&T (whose broadband business and stake in TWE was bought by Comcast) that owned the Warner Brothers film studio, HBO and the WB broadcast network. That would help clear up AOL's corporate structure, since it would give AOL full control of both the Warner Brothers and New Line Cinema studios.

Second, AOL Time Warner would most likely unload a portion of its colossal debt load ($28.3 billion as of Sept. 30) onto the cable unit. It could also use proceeds from the sale of the cable business to reduce debt.

In addition to the AOL online division and cable system, AOL Time Warner owns advertising-sensitive businesses such as cable networks CNN, TBS and TNT, and a magazine publishing business that includes Time, Fortune and Sports Illustrated. But the slowdown in the AOL dial-up Internet access business has received the most attention during the past year.

And a name change or spinoff would not do anything to address the decline in this division. Gilbert says one major positive about Case's resignation is that it will clearly give AOL Time Warner CEO Dick Parsons and his management team more flexibility to do whatever it takes to restore growth at AOL.

But with that comes added pressure since Case will no longer be around to be a scapegoat.

"I don't know if guidance is going to get much lower for AOL, but it still looks like it's kind of in a death spiral," says Gilbert. "If things are still deteriorating at AOL by late this summer, people are going to wonder whether or not Parsons can fix it as well."