Happy to share my 2cts as a pure LP investor (have never operated/syndicated/GPed a deal)...
When I receive distributions from a deal, either ON or OF the capital I originally invested, I decrease my risk exposure to the deal (as @Evan Polaski mentioned).
So if my initial investment was $100k and I received an accumulated amount of $40k back over time, my exposure at that point in time is $60k. Doesn't matter to me if the $40k was ON or OF capital, it's still money in the bank in my mind.
Yes, there are different tax implications to each type of distribution, but that's a different discussion.
Now the real question here is - What happens to future distributions if you've received return OF capital.
I'll explain what I mean here:
Let's say there is an 8% annual pref or CoC return on the investment example above.
This means that originally I should receive $8k per year (8% on $100k, distributed every quarter).
Now that I have received $40k return OF capital, do I get 8% on the remaining $60k? Or even more extreme - What happens if after a year I received my original $100k back as return OF capital. Do I get any type of annual distribution going forward?
I've seen so many different approaches to this it's crazy.
As an LP, I think the fairest model should be for the GP to distribute the annual profit, after keeping some money in the bank for worst case scenarios, and distribute the rest pro-rata with the LPs (or based an agreed upon waterfall).
Just my 2cts, I'm sure the others might be able to shed some light on this.