Recent advancements have demonstrated the advantage of converting pretrained large language models into powerful text encoders by enabling bidirectional attention in transformer layers. However, existing methods often require extensive training on large-scale datasets, posing challenges in low-resource, domain-specific scenarios. In this work, we show that a pretrained large language model can be converted into a strong text encoder without additional training. We first conduct a comprehensive empirical study to investigate different conversion strategies and identify the impact of the attention sink phenomenon on the performance of converted encoder models. Based on our findings, we propose a novel approach that enables bidirectional attention and suppresses the attention sink phenomenon, resulting in superior performance. Extensive experiments on multiple domains demonstrate the effectiveness of our approach. Our work provides new insights into the training-free conversion of text encoders in low-resource scenarios and contributes the advancement of domain-specific text representation generation. Our code is available at https://github.com/bigai-nlco/Look-Both-Ways-and-No-Sink.