Open science is a practice that makes scientific research publicly accessible to anyone, hence is highly beneficial. Given the benefits, the software engineering (SE) community has been diligently advocating open science policies during peer reviews and publication processes. However, to this date, there has been few studies that look into the status and issues of open science in SE from a systematic perspective. In this paper, we set out to start filling this gap. Given the great breadth of SE in general, we constrained our scope to a particular topic area in SE as an example case. Recently, an increasing number of deep learning (DL) approaches have been explored in SE, includingDL-based software vulnerability detection, a popular, fast-growing topic that addresses an important problem in software security. We exhaustively searched the literature in this area and identified 55 relevant works that propose a DL-based vulnerability detection approach. This was then followed by comprehensively investigating the four integral aspects of open science:availability,executability,reproducibility, andreplicability. Among other findings, our study revealed that only a small percentage (25.5%) of the studied approaches provided publiclyavailabletools. Some of these available tools did not provide sufficient documentation and complete implementation, making them notexecutableor notreproducible. The uses of balanced or artificially generated datasets caused significantly overrated performance of the respective techniques, making most of them notreplicable. Based on our empirical results, we made actionable suggestions on improving the state of open science in each of the four aspects. We note that our results and recommendations on most of these aspects (availability,executability,reproducibility) are not tied to the nature of the chosen topic (DL-based vulnerability detection) hence are likely applicable to other SE topic areas. We also believe our results and recommendations onreplicabilityto be applicable to other DL-based topics in SE as they are not tied to (the particular application of DL in) detecting software vulnerabilities.