They're a constant problem in all browsers. Take last year's Pwn2Own for example: http://blog.trendmicro.com/pwn2own-day-2-event-wrap/

Demonstrated a successful code execution attack against Safari to gain root privileges using an use-after-free vulnerability in Safari and an out-of-bounds vulnerability in Mac OS X.

Demonstrated a successful code execution attack against Microsoft Edge in the SYSTEM context using an uninitialized stack variable vulnerability in Microsoft Edge

Demonstrated a successful code execution vulnerability against Microsoft Edge in the SYSTEM context using an out-of-bounds vulnerability in Microsoft Edge and a buffer overflow vulnerability in the Kernel.

etc. Highlights mine. All of these are prevented in safe Rust.