The main reason integer overflow often turns into a vulnerability is because the overflowed result is either used to index into allocated memory, or as the size of a memory allocation which will later be indexed into. In both of these cases, the vulnerability can be prevented by bounds checking every access into memory, as Rust does (except on a few methods which can only be used within an "unsafe" block).

Another reason integer overflow can turn into a vulnerability is because it's Undefined Behavior, and when encountering Undefined Behavior the compiler can do anything, including eliding bounds checks. Rust (and C with -fno-strict-overflow) prevents that by making integer overflow have a defined behavior.