An assertion is commonly used to validate the expected programs behavior (e.g., if the returned value of a method equals an expected value) in software testing. Although it is a recommended practice to use only one assertion in a single test to avoid code smells (e.g., Assertion Roulette), it is common to have multiple assertions in a single test. One issue with tests that have multiple assertions is that when the test fails at an early assertion (not the last one), the test will terminate at that point, and the remaining testing code will not be executed. This, in turn, can potentially reduce the code coverage and the performance of techniques that rely on code coverage information (e.g., spectrum-based fault localization). We refer to such a scenario as early test termination. Understanding the impact of early test termination on test coverage is important for software testing and debugging, particularly for the techniques that rely on coverage information obtained from the testing. We conducted the first empirical study on early test termination due to assertion failure (i.e., early test termination) by investigating 207 versions of 6 open-source projects. We found that a nonnegligible portion of the failed tests (19.1%) is early terminated due to assertion failure. Our findings indicate that early test termination harms both code coverage and the effectiveness of spectrum-based fault localization. For instance, after eliminating early test termination, the line/branch coverage is improved in 55% of the studied versions, and improves the performance of two popular SBFL techniques Ochiai and Tarantula by 15.1% and 10.7% compared to the original setting (without eliminating early test termination) in terms of MFR, respectively.