Try using Paste Special; there should be an option for Unicode text.

Note that if the source document was created with a Symbol font, this won't help. Windows doesn't really know that the character is related to a specific Unicode character, the symbol fonts were created before Unicode as a way of meeting a need and the two aren't interchangeable.

In addition to DrZoo's answer, there is a second possibility of where the error comes from: Your curent font does not have a glyph for the fox. Especially since Emojis are new-ish and low on the priority of font-makers, it is quite likely that your font simply cannot provide a symbol, in which case notepad++ defaults to the square you see.

Check what font you have and then verify that it indeed has emojis, or switch to a font known for having them. One of these would be "consolas", which is used here on stackexchange (and given that you do have the fox in your post, we know that it includes the symbol you need)

We strip out non-printable characters except for TAB, CR, and LF.

I can see how this could be a problem for a few cases, but these cases are fairly rare, so I believe those questions/answers can still be posted but with non-printable characters explicitly replaced with other symbols for the sake of readability.

While searching for something entirely different in the Arial MS Unicode glyph set in Adobe InDesign, I came across this section:

This shows that there is a dedicated set of Unicode Code points for the control characters, and indeed looking it up on Unicode.org you can find them in code block U+2400.

This gives you a Unicode code point to look for in a font's list of supported glyphs. FileFormat.info lists, amongst others: Arial Unicode MS, Code2000, and Segoe UI Symbol. Unfortunately, none of the fonts listed have the dotted outline of your example.

If you don't mind using Flash, it seems FileFormat can check your local font set, and so determine if the symbols indeed do come ready and all out of one of your locally installed fonts, or possibly from somewhere else.

The only way to be sure a browser can display a international run of text is to use web fonts. For an app it's a bit simpler as you can bundle the font with the app and install it at the same time.

In both cases you need to check the licensing of the chosen font allows the kind of distribution you envision. So not really suitable for a general-purpose password generator.

Be aware that many unicode combinations won't be type-able except with very specific keyboard layouts /input methods. So you'll be forcing the user to copy and paste passwords he can not type.

Lastly, an unicode encoding point won't necessarily correspond to a single symbol. Many encoding points are combining symbols that can only be used with specific other symbols in specific orders.

You should really start by adding "simple" unicode blocks such as basic greek or cyrillic letters, the dingbat block, arrows and engineering symbols, avoid anything combining, avoid ligatures, diacritics, complex asian scripts etc.

Greek and cyrillic in particular should be supported by most modern systems without addons. They require so few symbols compared to most asian scripts only the most rabid barebone system will skip them.

Dingbat and arrows/engineering symbols will require specific fonts to be sure of support but those are easy to find (for exemple, in symbola) and this kind of symbol won't require a text engine capable of complex text. Avoid math symbols or carefully screen them, quite a lot of them combine fileformat.info will tell you which symbol is available in common fonts. That requires knowing which font ship with which OS, and to be aware of font versions (a later version of the same font may include more glyphs, but few systems update the fonts they shipped with).

That should be sufficient to strengthen your generator without hitting strange corner cases.