Interpret numbers very literally

Python 2, 76 bytes

f=lambda n,k=1000:n>19and(f(n/k,k/10)+`k-k%4*5`)*(n>=k)+f(n%k,k/10)or`n`[:n]

Try it online!

Test suite from Chas Brown.

A fully recursive solution that splits on place values k=1000, k=100, and k=10. The separator for the place values is computed as k-k%4*5, which maps

1000 -> 1000
100  -> 100
10   -> 0

By stopping when n<=19, we avoid one-word numbers in the teens being split up.

Gaia, 44 43 bytes

:(!>
ℍZ:₸Z¤1>∧'0פṙ$×:dẏ×,↑ℍṙ×
@3eZ,↑¦↓3eṙ×

Longer than my original answer, but it works now.

fixed my code again but now it's twice as sad

Try it online!

@3eZ,↑¦↓3eṙ×  Main function.
@3eZ          Input divmod 1000, pushes input div 1000 then input mod 1000
    ,         Pair those two value into a list
     ↑¦       Run the upper function on both
       ↓      Call the function below (loops to top function)
        3eṙ   The string "1000"
           ×  Join the list with "1000"

ℍZ:₸Z¤1>∧'0פṙ$×:dẏ×,↑ℍṙ×  Helper function. Called with 1 argument.
ℍZ                          Divmod with 100
  :₸Z                       Copy the mod part and divmod with 10
                            Stack is: [100s digit, arg mod 100, 10s digit, 1s digit]
     ¤1>                    Bring 10s digit to the top and check if it's greater than 1
        ∧                   Logical AND with 1s digit. (results in 0 or 1)
         '0×                Multiply the character 0 by that result
            ¤               Bring 'arg mod 100' to the top
             ṙ$             Get its string representation and split it into characters
                            (simply doing digit list doesn't work in the case it's 0)
               ×            Join this with the multiplied '0' string
                :d          Copy and parse as a number
                  ẏ         Is it positive? (0 or 1)
                   ×        Multiply the string of the number by that result.
                    ,       Pair: gives the list [100s digit, string from above]
                     ↑      Call the function above
                      >     Remove the first ^ elements from the pair
                       ℍṙ×  Join the resulting list with the string "100"

:(!>  Helper function 2. In this program it is only called with a list.
:(    Copy and get the first element.
  !   Boolean negate (0 or 1)
   >  Remove that many characters from the start of the list

Python 3+inflect, 193 bytes

import inflect,re
exec("for i in re.sub('(and)|\W',' ',%sinput())).split():\n for j in range(0,6**8):\n  if i in %sj):\n   print(j,end='')\n   break"%(('inflect.engine().number_to_words(',)*2))

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Very naive solution which uses Python's inflect library. Here is the unfurled code:

import inflect,re
for i in re.sub('(and)|\W+',' ',inflect.engine().number_to_words(input())).split():
 for j in range(0,6**8):
  if i in inflect.engine().number_to_words(j):
   print(j,end='')
   break