tree-stderr.sh

#!/bin/sh

foo ()
{
    echo stdout
    echo stderr 1>&2
    return 1
}

{
    {
        {
            # 1. Copy stdout to 3 and stderr to stdout (1)
            thing 2>&1 1>&3
            # 2. Print exit status to 4
            echo $? 1>&4
            # 3. Our stdout is original stderr, so we can capture error messages
        } | tee ./errors
        # 4. Copy 1 (originbal stderr) to back 2
        #    Copy 4 to 1, read it and produce exit status
    } 4>&1 1>&2 | ( read -r STATUS; exit "$STATUS" )
    # 5. Copy 3 (original stdout) back to 1
} 3>&1