While it is not part of the memory safety guarantee of safe Rust, in practice it is much harder to accidentally leak memory in Rust than in C++. There is no counterpart to the C++ new operator in Rust; no commonly-used language feature or standard library function puts the burden of explicitly freeing memory on the programmer.

For those who are interested in why leaking memory isn't disallowed by Rusts safety guarantees, have a look at the documentation of the (AFAIK) only safe function in the standard library that leaks memory: https://doc.rust-lang.org/std/mem/fn.forget.html