GREP rules are more powerful than Indesign's Drop Caps feature, and can do this. You add them in much the same way, via paragraph styles, and you choose what character style to apply to the text that matches the rule.
The downside is, they're harder to set up... It looks like voodoo at first. But clicking on the @ icon you can browse the possible options and tick 'Preview' to trial-and-error it until you get a rule that works. It's not as scary as it looks, but it does involve some head-scratching and can involve a lot of trial and error.
Here's a few handy GREP rules that might do what you want:
- Last character of the paragraph:
$ = end of paragraph,
. = one of any character)
- Last 4 characters of the paragraph:
- (four repetitions
. at the end of the paragraph
- Last word of the paragraph:
- (from a whitespace character
\s, if there's a chunk of non-whitespace characters
[^\s]* that reaches the end of the paragraph
$, grab it)
- Last letter or number in the paragraph:
- (any one of
 a digit
\l or uppercase
\u that is followed by
(?=) any number of
* things that aren't digits, lowercase or uppercase that are at the end of the paragraph
If you want some equivalent specifically of the multi-line feature drop caps have, where text wraps around the styled character, that's quite tricky. Text can't flow around things that are ahead of it in the text, so you can't make this happen completely automatically.
But you can make things like this, that move and flow with the text as you add more text, with only a little manual work:
- Create a text frame of the size of your 'drop-cap' (in CS6 you can set it to Auto-Size in Text Frame properties). Put the character in, give it a style of the right size, etc.
- Cut the text frame, put the text cursor at the start of your paragraph, paste.
- Select the smaller frame, right-click,
Anchored object > Custom.
- Set the anchored position to X relative to Text Frame, 0 offset, reference point on the right
- Leave "Prevent manual positioning" unticked, hit okay, and drag it down to the end of the paragraph.
- (unfortunately if you just place the anchor at the end of the paragraph, the text can't wrap around it... a long standing annoying bug/limitation)
- Make sure it has text wrap from the Text Wrap window, so text wraps around it. Add any padding here if needed.
- When you need more of these, copy and paste this frame (selecting it and pasting it as text with the type tool, not selecting the frame directly) then move it down to the end of the paragraph. Or, you can save this as an object style.