WebAssembly (Wasm) is a next-generation portable compilation target for deploying applications written in high-level languages on the web. In order to protect their memory from untrusted code, web browser engines confine the execution of compiled Wasm programs in a memory-safe sandbox. Unfortunately, classic memory-safety vulnerabilities (e.g., buffer overflows and use-after-free) can still corrupt the memory within the sandbox and allow Wasm code to mount severe attacks. To prevent these attacks, we study a class of secure compilers that eliminate (different kinds of) of memory safety violations. Following a rigorous approach, we discuss memory safety in terms of hypersafety properties, which let us identify suitable secure compilation criteria for memory-safety-preserving compilers. We conjecture that, barring some restrictions at module boundaries, the existing security mechanisms of Wasm may suffice to enforce memory-safety preservation, in the short term. In the long term, we observe that certain features proposed in the design of a memory-safe variant of Wasm could allow compilers to lift these restrictions and enforce relaxed forms of memory safety.