You can't make a language "idiot proof" but by changing how we think about the problem we can make a huge difference.
The trick is, what programs do we even want to exist? There's no need to be able to write all the programs you didn't want. In Rust, such programs get consigned to unsafe, which means that yes, sometimes to do general purpose programming (and especially e.g. in Rust's own stdlib) you must use unsafe Rust. But it already means we can constrain "idiots" (or more reasonably, new programmers) to safe Rust and rule out all those problems that aren't in the reduced domain of safe Rust.
You can go much further than Rust. WUFFS isn't a general purpose language at all. While a Rust compiler written entirely in Rust isn't a priority it'll likely happen sooner or later, but a WUFFS compiler written in WUFFS is nonsense, WUFFS doesn't even have strings. WUFFS is for, well, Wrangling Untrusted File Formats Safely, hence the name. Notice not files just the file format. WUFFS has no idea what a file is, no file APIs, since it doesn't know what strings are it couldn't easily name files anyway. But inside its domain WUFFS gets to be 100% safe while also being faster than code you'd actually write in other languages.
Take buffer overflow buffer[n]. In a language like C++ direct access isn't bounds checked and so overflows are common when n is too large, too dangerous. OK, in a language like (safe) Rust this access is bounds checked, now the overflow is prevented when n is too large but the bounds check cost CPU cycles, a little slower.
WUFFS doesn't do either, in WUFFS that variable n was used to index into buffer therefore n is constrained to be 0 and no bounds checking.
A complete idiot's WUFFS GIF decoder might be wrong - it could report spurious decoding errors, it could decode a blue dog as a pink roller skate, render images upside down or even decode JPEG instead of GIF - whatever, but it can't escape the limits of WUFFS itself. It can't go off piste and send your password database to a remote HTTP server or delete all your logs, or send spam emails or run some machine code it found inside the supposed GIF file.