While Compute Express Link (CXL) enables support for cache-coherent shared memory among multiple nodes, it also introduces new types of failures--processes can fail before data does, or data might fail before a process does. The lack of a failure model for CXL-based shared memory makes it challenging to understand and mitigate these failures. To solve these challenges, in this paper, we describe a model categorizing and handling the CXL-based shared memory's failures: data and process failures. Data failures in CXL-based shared memory render data inaccessible or inconsistent for a currently running application. We argue that such failures are unlike data failures in distributed storage systems and require CXL-specific handling. To address this, we look into traditional data failure mitigation techniques like erasure coding and replication and propose new solutions to better handle data failures in CXL-based shared memory systems. Next, we look into process failures and compare the failures and potential solutions with PMEM's failure model and programming solutions. We argue that although PMEM shares some of CXL's characteristics, it does not fully address CXL's volatile nature and low access latencies. Finally, taking inspiration from PMEM programming solutions, we propose techniques to handle these new failures. Thus, this paper is the first work to define the CXL-based shared memory failure model and propose tailored solutions that address challenges specific to CXL-based systems.