The useful character that is none
twivorite.com
twivorite.com
Then I was able to paste it into SublimeText. I pasted it several times. SublimeText says the line is 6 characters long, but the cursor is still at the left edge! Then I copied that line, and my clipboard viewer shows 14 bytes for the Unicode entry, 12 bytes for the 6 characters and a two null bytes. As expected, the characters survive being saved with Trim Trailing Whitespace enabled. Reopening the file with a single-byte encoding (I tried Windows 1252) showed the characters. My hex viewer shows 6 occurrences of E2 80 8B.
Unfortunately, there's a lot of blurred lines and loose usage of terminology due to misunderstandings and historical baggage (e.g. ambiguous usage of "charset", Microsoft's usage of "Unicode", "ASCII" used to refer to both charset and encoding, etc.) which contributes to the confusion.
Hacker News also disallows this in its comments. YMMV with other non-printing characters.
It doesn’t work in Safari on iOS, FWIW.