Automatic exercisions can be extremely risky, and the closer to the money the options are, the riskier their exercisions are.
It is unlikely that the entire account has negative equity since a responsible broker would forcibly close all positions and pursue the holder for the balance of the debt to reduce solvency risk. Since the broker has automatically exercised a near the money option, it's solvency policy is already risky.
Regardless of whether there is negative equity or simply a liability, the least risky course of action is to sell enough of the underlying to satisfy the loan by closing all other positions if necessary as soon as possible.
If there is a negative equity after trying to satisfy the loan, the account will need to be funded for the balance of the loan to pay for purchases of the underlying to fully satisfy the loan.
Since the underlying can move in such a way to cause this loan to increase, the account should also be funded as soon as possible if necessary.
Accounts after exercise
For deep in the money exercised options, a call turns into a long underlying on margin while a put turns into a short underlying.
The next decision should be based upon risk and position selection. First, if the position is no longer attractive, it should be closed. Since it's deep in the money, simply closing out the exposure to the underlying should extinguish the liability as cash is not marginable, so the cash received from the closing out of the position will repay any margin debt.
If the position in the underlying is still attractive then the liability should be managed according to one's liability policy and of course to margin limits.
In a margin account, closing the underlying positions on the same day as the exercise will only be considered a day trade. If the positions are closed on any business day after the exercision, there will be no penalty or restriction.
Cash option accounts
While this is possible, many brokers force an upgrade to a margin account, and the ShareBuilder Options Account Agreement seems ambiguous, but their options trading page implies the upgrade.
In a cash account, equities are not marginable, so any margin will trigger a margin call. If the margin debt did not trigger a margin call then it is unlikely that it is a cash account as margin for any security in a cash account except for certain options trades is 100%.
Equities are convertible to cash presumably at the bid, so during a call exercise, the exercisor or exercisor's broker pays cash for the underlying at the exercise price, and any deficit is financed with debt, thus underlying can be sold to satisfy that debt or be sold for cash as one normally would.
To preempt a forced exercise as a call holder, one could short the underlying, but this will be more expensive, and since probably no broker allows shorting against the box because of its intended use to circumvent capital gains taxes by fraud. The least expensive way to trade out of options positions is to close them themselves rather than take delivery.
