In the end it's possible in any language to produce exploitable bug (apart from maybe Erlang VM?). The point is about 1) how hard (probable) it is, 2) how popular are error checking tools (C static analyzers, Google Thread Sanitizer, etc), and 3) how fast can the culprit code be found and fixed.

In that regard Rust has reduced both 1) and 3) by only exposing dangerous features in unsafe {}, and greatly improved 2) since the compiler itself is checking those errors.