You seem to be presupposing a particular solution in your question. Only in your second paragraph do you tell us what your question is. Your real question is "Sometimes when we send a PDF document to print, some of the characters/fonts don't print correctly. Why is this and how do we fix it?"
Trying to understand the internal structure of a PDF for a problem like this is somewhat of a fool's errand. I would recommend instead that you let the person answering the question propose a solution, rather than asking why the solution that you think should work is not working.
Anyway, some background information.
In every PDF, there are two types of fonts: embedded fonts, and referenced fonts.
Embedded fonts are contained in their entirety within the PDF itself. Any compatible PDF reader program should be able to print every character of an embedded font. If it can't, that's a separate problem. The advantage is that you can use custom fonts and the person viewing/printing the document will be able to read the fonts whether or not they have that font installed on their computer.
Referenced fonts are fonts that are only referred to "by name" within the PDF document, but the PDF relies on the operating system to have the font files present at the time of rendering/printing, or you get "font problems" like you said. The advantage is small file size.
The possible problems you could be having are many, and I can't tell which problem you are having from your question, so I'll enumerate them along with possible resolutions:
Your fonts could be embedded in the PDF, but your PDF printer/renderer could be having a problem parsing (using) the font(s). This is typically a bug specific to a piece of software, or perhaps it is incompatible with the font file format that is embedded. You can resolve this problem usually by upgrading your PDF printing software, and you should verify that the PDF renders correctly on a canonical PDF viewer such as Adobe Reader (the latest version) on Windows, prior to taking any corrective action.
Your fonts could be referenced in the PDF, but your PDF printer does not have that font available. You can resolve this problem by either (a) installing the appropriate font(s) on the computer/device that prints or renders the PDF, or (b) switching over your PDF creation software to embedding the fonts in the PDF rather than referencing them.
You can detect which fonts are referenced and which fonts are embedded by a number of ways (depending on your platform, etc) -- see this StackOverflow question. The first thing you can do is configure the software that generates the PDFs to always embed all fonts. This will increase file size; if you can deal with the resulting file size, it should make printing much more reliable.
You could also determine whether each referenced font is available on the system, but that is platform-dependent, meaning that the solution for doing so would depend on which operating system you're running and what kind of software environment is available to you e.g. for programming.
Overall this is a very vague question and I don't think it is particularly answerable in its current form because of all the possible variables that may be causing this problem. You seem to be asking about the internals of a PDF in a very abstract way without reference to any particular piece of software or platform. I have provided this answer in the attempt to be helpful, but please be aware that this question could be closed if it is not made more specific.