Dead Code Elimination (DCE) is a fundamental compiler optimization technique that removes dead code (e.g., unreachable or reachable but whose results are unused) in the program to produce smaller or faster executables. However, since compiler optimizations are typically aggressively performed and there are complex relationships/interplay among a vast number of compiler optimizations (including DCE), it is not known whether DCE is indeed correctly performed and will only delete dead code in practice. In this study, we open a new research problem to investigate: can DCE happen to erroneously delete live code? To tackle this problem, we design a new approach named Xdead, which leverages differential testing, static binary analysis, and dynamic symbolic execution techniques, to detect miscompilation bugs caused by the erroneously deleted live code. Preliminary evaluation shows that Xdead can identify many divergent portions indicating erroneously deleted live code and finally detect two such miscompilation bugs in LLVM compilers. Our findings call for more attention to the potential issues in existing DCE implementations and more conservative strategies when designing new DCE-related compiler optimizations.