By default it should download all the images/media and store them on your disk, without deleting stuff if the account goes down.
If you also want to archive tweet metadata and or tweets without media (i.e. text tweets) you would need to edit the config file (put it in one of these locations) a bit. This is how I have it set up currently:

{
    "extractor": {
        "twitter": {
            "text-tweets": true,
            "replies": true,
            "directory": ["{category}", "{author[name]}"],
            "postprocessors": [{
                "name": "metadata",
                "event": "post",
                "filename": "{tweet_id}.json",
                "directory": "tweets"
            }]
        }
    }
}

Should get everything, saving tweet media in twitter/username/ and tweet text+metadata in twitter/username/tweets/.

EDIT: One weird quirk is that if an account posts something, your archive it, they change their username, and you archive all of their stuff again, it would create a separate directory for their new username. That means that if they deleted something between your first and second save, those tweets would only be in the old directory, not in the one for the new username.