Would shareholder’s equity ever be greater than market capitalization?

Yes, this is possible if the stock price has declined so much that the market capitalization, calculated as # of shares x stock price, is lower than the original book value of shareholder’s equity. The book value of shareholder’s equity is recorded at the amount of the initial investment.

In other words, the market value of the investment can be lower than the initial investment amount because of factors such as lower revenue forecasts, higher costs, higher risks, bankruptcy and any factors that could contribute to a stock selloff.