It looks like each of the distributions over the last several years have consisted entirely of capital gains, and I wouldn't expect the fund to start distributing paid-in capital to shareholders in the near term. But it is not inconceivable that the fund may at some point in the future have to distribute some of the capital that will be raised in this rights offering back to shareholders. I'm not saying that this will happen, just that it is possible.
As long as a fund is distributing either dividend income or capital gains to shareholders, I don't think there is anything wrong with it raising new money at the same time that it has a high distribution policy. But if there is a return of capital included in the distributions, investors will wonder why they gave the fund additional money just to have it returned to them. It could happen in a situation where the fund manager wants to have more assets on which to collect management fees, but also wants to have a high distribution yield to keep the discount low and ward off activist investors. While this does not appear to be an issue with HQL, I could see it being a problem for other funds someday.
HQL 1-yr chart: