Software maintenance is one of the most cost-intensive phases in the software development lifecycle. A prevalent and paradoxical phenomenon — wherein the act of fixing a defect inadvertently introduces one or more new defects — significantly undermines software quality and reliability. These newly introduced defects, commonly termed regression bugs or fix-inducing changes, account for a substantial portion of post-release failures. This paper presents a comprehensive review of the causes, patterns, and mitigation strategies associated with bug-fix- induced regressions. We examine the theoretical foundations of software coupling and co-change dependencies, analyze empirical studies across open-source and industrial codebases, and survey state-of-the-art techniques including regression test selection, change impact analysis, automated patch validation, and AI-assisted code review. Our review identifies that insufficient test coverage, poor change impact analysis, high code coupling, and developer cognitive overload are the primary contributors to regression introduction. We further discuss the role of technical debt and architectural erosion in amplifying this phenomenon.