Fixing bugs is an important phase in software development and maintenance. In practice, the process of bug fixing may conflict with the release schedule. Such confliction leads to a trade-off between software quality and release schedule, which is known as the technical debt metaphor. In this article, we propose the concept of debt-prone bugs to model the technical debt in software maintenance. We identify three types of debt-prone bugs, namely tag bugs, reopened bugs, and duplicate bugs. A case study on Mozilla is conducted to examine the impact of debt-prone bugs in software products. We investigate the correlation between debt-prone bugs and the product quality. For a product under development, we build prediction models based on historical products to predict the time cost of fixing bugs. The result shows that identifying debt-prone bugs can assist in monitoring and improving software quality.