How can I save a Word document as a PDF *without* any embedded fonts?

It is possible to remove all the fonts forming xml document type WordML.

<?xml version="1.0" encoding="UTF-8"?>
<?mso-application progid="Word.Document"?>
    <w:wordDocument xml:space="preserve" xmlns:w="http://schemas.microsoft.com/office/word/2003/wordml">
     <w:body>

      <w:tbl>
       <w:tblPr>
        <w:tblW w:w="9570" w:type="dxa"></w:tblW>
         <w:tblBorders> <w:top w:val="nil" /><w:left w:val="nil" /><w:bottom w:val="nil" /><w:right w:val="nil" />
         </w:tblBorders>
       </w:tblPr>

    <w:tr>
     <w:tc>
    <w:tcPr><w:tcW w:w="4785" w:type="dxa" /></w:tcPr>  <w:p></w:p>  </w:tc>
     <w:tc>  
    <w:tcPr><w:tcW w:w="4785" w:type="dxa" /></w:tcPr>  <w:p></w:p>  </w:tc>
    </w:tr>   

     <w:tr>    
         <w:tc>
          <w:tcPr><w:tcW w:w="0" w:type="auto" /></w:tcPr>  <w:p><w:pPr><w:jc w:val="right" /></w:pPr>
       <w:r><w:t>Company: </w:t></w:r> 
      </w:p>
     </w:tc>   

        <w:tc>
          <w:tcPr><w:tcW w:w="0" w:type="auto" />
           <w:tcBorders>      <w:top w:val="single" w:sz="2" w:color="0070C0" />    <w:left w:val="single" w:sz="2" w:color="0070C0" /> <w:bottom w:val="single" w:sz="2" w:color="0070C0" /> <w:right w:val="single" w:sz="2" w:color="0070C0" />
           </w:tcBorders>
          </w:tcPr>
         <w:p><w:pPr><w:jc w:val="left" /></w:pPr><w:r><w:t></w:t></w:r></w:p>
        </w:tc>      
       </w:tr>       
      </w:tbl>
     </w:body>
    </w:wordDocument>

But, even if you delete all the styles and fonts of the original document, Word will assign during the opening of the document style by default. Also, at least one font will be in the Acrobat document when you open it, as if you did not act.

Office WordML XML File, Word load default style:

After save as PDF in Acrobat view one font

A good solution is to choose at least one font that will still be in the pdf file and use it.

Way 2: Removing Unused Styles from Word

Sub DeleteUnusedStyles()
    Dim oStyle As Style
    For Each oStyle In ActiveDocument.Styles
        ‘Only check out non-built-in styles
        If oStyle.BuiltIn = False Then
            With ActiveDocument.Content.Find
                .ClearFormatting
                .Style = oStyle.NameLocal
                .Execute FindText:=””, Format:=True
                If .Found = False Then oStyle.Delete
            End With
        End If
    Next oStyle
End Sub 

See Format Fonts for Text Field Default Values

Style almost always includes the font and font size used for the determination of other sizes. Paragraph, line spacing, and so on ... If you need a different style mechanics generate the document itself. Including substitute fonts. If the final PDF document then use the built-in Adobe JavaScript. Or Adobe LiveCycle Designer ES and XDP XML.

Using Acrobat JavaScript in Forms: Importing and Exporting Form Data

XML Forms Architecture PDF!