Cross-Domain Sequential Recommendation (CDSR) methods aim to address the data sparsity and cold-start problems present in Single-Domain Sequential Recommendation (SDSR). Existing CDSR methods typically rely on overlapping users, designing complex cross-domain modules to capture users' latent interests that can propagate across different domains. However, their propagated informative information is limited to the overlapping users and the users who have rich historical behavior records. As a result, these methods often underperform in real-world scenarios, where most users are non-overlapping (cold-start) and long-tailed. In this research, we introduce a new CDSR framework named Information Maximization Variational Autoencoder (\textbf{\texttt{IM-VAE}}). Here, we suggest using a Pseudo-Sequence Generator to enhance the user's interaction history input for downstream fine-grained CDSR models to alleviate the cold-start issues. We also propose a Generative Recommendation Framework combined with three regularizers inspired by the mutual information maximization (MIM) theory \cite{mcgill1954multivariate} to capture the semantic differences between a user's interests shared across domains and those specific to certain domains, as well as address the informational gap between a user's actual interaction sequences and the pseudo-sequences generated. To the best of our knowledge, this paper is the first CDSR work that considers the information disentanglement and denoising of pseudo-sequences in the open-world recommendation scenario. Empirical experiments illustrate that \texttt{IM-VAE} outperforms the state-of-the-art approaches on two real-world cross-domain datasets on all sorts of users, including cold-start and tailed users, demonstrating the effectiveness of \texttt{IM-VAE} in open-world recommendation.