Cost basis of inherited stocks is the value on the date of death of the prior owner. If sold on that date (nearly impossible) there would be zero capital gain. Given the current state of the markets the value of her stock has probably decreased which would result in a capital loss rather than a gain. Capital losses are tax deductible, but the net loss (gains minus losses) allowed each year is limited to $3,000 with any additional loss being carried forward to the next tax year.

It's difficult to guess whether selling at this time to cover debt would make sense or not. It depends on what the stocks are. If she owns Financials or Automotive, I'd bail now. If it's IBM, Exxon, Praxair, or other major international manufacturers I'd hang on to it until the current round of carnage is over. Some stocks are beaten down just because the markets are in pain, even though the companies have very stong balance sheets, revenue, etc.

So the real answer to your question is 'maybe'. It sounds like there is limited experience to draw on, so perhaps the best solution is to make use of an experienced financial advisor that has no interest in anything you may sell and is only providing guidance. I would never use a bank or stock broker for this advice.

JohnG