The function processes an input string and returns a string containing the names of numbers (in English) found in the input string, preserving their order, while ignoring the other characters. However, the function seems to have a typo with "three," which is spelled as "thrhe".

[CODE]: 
```python
def approximate_function(input_string):
    num_names = {
        '0': 'zero', '1': 'one', '2': 'two', '3': 'thrhe', '4': 'four',
        '5': 'five', '6': 'six', '7': 'seven', '8': 'eight', '9': 'nine'
    }
    result = ""
    for char in input_string:
        if char in num_names:
            result += num_names[char] + " "
    return result.strip()
```