Develop a Python script that uses the Twitter API to fetch the latest tweets from a specified user and saves them into a text file. The script should also include error handling for cases where the user does not exist or the API limit is reached.

To create a Python script that fetches the latest tweets from a specified user and saves them into a text file, you'll need to have Tweepy library installed. If you don't have it installed, run:

```bash
pip install tweepy
```

Then, follow these steps:

1. Create a Twitter Developer account and obtain your API keys and access tokens: https://developer.twitter.com/en/apps

2. Replace `API_KEY`, `API_SECRET_KEY`, `ACCESS_TOKEN`, and `ACCESS_TOKEN_SECRET` in the code below with your own credentials.

3. Save the following code as `fetch_tweets.py`.

```python
import tweepy
import sys

def get_api():
    API_KEY = 'your_API_KEY'
    API_SECRET_KEY = 'your_API_SECRET_KEY'
    ACCESS_TOKEN = 'your_ACCESS_TOKEN'
    ACCESS_TOKEN_SECRET = 'your_ACCESS_TOKEN_SECRET'

    auth = tweepy.OAuthHandler(API_KEY, API_SECRET_KEY)
    auth.set_access_token(ACCESS_TOKEN, ACCESS_TOKEN_SECRET)

    api = tweepy.API(auth, wait_on_rate_limit=True, wait_on_rate_limit_notify=True)
    return api


def save_tweets_to_file(screen_name):
    try:
        api = get_api()
        tweets = api.user_timeline(screen_name=screen_name, count=200, tweet_mode='extended')

        if not tweets:
            print(f"No tweets found for user {screen_name}")
            return

        with open(f"{screen_name}_tweets.txt", "w", encoding="utf-8") as f:
            for tweet in tweets:
                f.write(tweet.full_text + "\n\n")

        print(f"Successfully saved tweets of {screen_name} to {screen_name}_tweets.txt")
    except tweepy.TweepError as e:
        if e.api_code == 50 or e.api_code == 63:
            print("User not found or suspended.")
        elif e.api_code == 88:
            print("Rate limit exceeded. Please wait before trying again.")
        else:
            print(f"An error occurred: {e}")


if __name__ == "__main__":
    if len(sys.argv) != 2:
        print("Usage: python fetch_tweets.py <screen_name>")
    else:
        screen_name = sys.argv[1]
        save_tweets_to_file(screen_name)
```

4. Run the script with a specified user's screen name:

```bash
python fetch_tweets.py example_user
```

This will create a text file named `example_user_tweets.txt` containing the latest tweets from the specified user.

Remember to handle API rate limits and errors gracefully, as shown in the code above.