It seems that it’s now fairly trivial to implement this. The Signal handling section of Command Line Applications in Rust goes over the concept, and mentions the ctrlc crate to handle that specific signal, and the signal-hook crate to handle signals in general.

Via the guide, with signal-hook it should be as simple as:

use std::{error::Error, thread};
use signal_hook::{iterator::Signals, SIGTERM};

fn main() -> Result<(), Box<Error>> {
    let signals = Signals::new(&[SIGTERM])?;

    thread::spawn(move || {
        for sig in signals.forever() {
            println!("Received signal {:?}", sig);
        }
    });

    Ok(())
}