Which is no different at all from what happens with a balanced portfolio.
Whether I choose to sell a portion of the value of my portfolio some years to provide cash flow, or the company decides to sell off a portion of the value of its stock to issue a dividend - it's the same (other than likely tax advantages to LTCG) .
There's no evidence that a high-div paying portfolio is any more stable or protected against failure than a balanced, diversified portfolio. It's likely that by picking high-div stocks, you are less diversified, which could be a problem.