As an increasing number of software systems reach sizes of hundreds of millions of lines of code, relying solely on code-level abstractions is impractical, posing profound challenges to software maintenance. Java Module Platform System (JPMS) provides architectural abstractions that enable Java engineers to control the required and provided interfaces of a module. Despite numerous advantages of enforced strong encapsulation provided by JPMS, developers still break those encapsulations to access the internal elements of a module. Such practice is referred to as Breaking the Strong Encapsulation (BSE). This behavior not only complicates the migration to newer versions (e.g., Java 9) but also threatens the integrity and safety of software projects. Since the BSE problem is still underexplored, in this work, we conduct the first empirical study to identify and characterize this widespread and impactful problem. We first collect a comprehensive dataset containing 4,079 GitHub issues and then investigate those issues from various perspectives, including symptoms, abuse sources, desired functionalities, and resolutions. Our empirical study highlights a tension in the Java module system: module developers aim to enforce strong encapsulation while module users frequently attempt to break the encapsulation. Our finding also emphasizes the need for both practitioners and researchers to develop effective strategies to mitigate these problems, offering an understanding of BSE characteristics to inform future detection and repair efforts.