Can a shareholder sell shares at a much lower rate than purchase price or at par value? eg. purchased at 100/share, sell at 0.01

We have a shareholder who purchased shares at 100/share. He wants to exit the company, which is a failed start-up. Realizing the loss of his investment, he just wants to exit with no further expenses. Can the company purchase his shares back at the par value of 0.01, by mutual agreement? Or does the company have to purchase them back at their purchase price. The company has no profit or income, only investments via the sale of shares and operating expenses.