Okay, there has always been some confusion between sub-domains and the parent domain. For the minute, forget any of the quotes you have read from Google and otherwise. It is not that these quotes are wrong, they are often misleading or often misinterpreted.
I will remove the confusion so that you understand.
From a search perspective, a sub-domain and the parent domain are separate sites. Why? To begin, the URLs are different and everything in a search engine is keyed off of the URL and the domain name reference. A URL contains 4 basic parts; the domain name reference, path, file, and parameters. In this case, we are only concerned with the domain name reference.
Let us say that a link to a page sub-domain.example.com/jackson_browne/rock_and_roll_icon.html has never been seen and is followed by the googlebot. The link is stored in a link index. The target URL is fetched, stored, and the domain name reference portion of the link sub-domain.example.com is copied the domain index and associated with the stored HTML code. The domain name portion is examined and recognized as a sub-domain. This parent domain name example.com is extracted and placed into the domain index and a link between sub-domain.example.com and example.com is made within the index. So for one link, we have two URLs, one fetched page, and one link.
The problem is that sub-domains are missing a lot of metrics the search engine needs. This is primarily because registration information does not exist for a sub-domain but does for the parent domain. Google begins to develop domain level metrics for example.com.
In the question, Do subdomains help/hurt SEO? the answer from Jeff Atwood quotes Vanessa Fox from http://www.searchenginejournal.com/subdomains-or-subfolders-which-are-better-for-seo/6849/ where she says Google is no longer treating subdomains (blog.widgets.com versus widgets.com) independently, instead attaching some association between them. The ranking algorithms have been tweaked so that pages from multiple subdomains have a much higher relevance bar to clear in order to be shown.. This is both true and false. It is misleading.
Google has never confused sub-domains from parent domains. These were always treated as separate sites because they are. The sub-domains and the parent domain have always been linked/associated within the domain index. Sub-domains have always inherited domain level metrics from the parent domain. What was new, at least at the time, is that the algorithm has been changed to further advantage Google in evaluating and ranking sub-domains closer to how parent domains are evaluated and ranked.
Now onto your scenario.
For your parent domain, while Google does have some domain level metrics, is missing metrics normally given to a site with content. This would be metrics from not only evaluating content, but links too. The missing metric values support some level of trust and value for the parent domain. Since these metrics do not exist, their value cannot be passed from the parent to the sub-domain, however, passing values is not a one-way street. Some value is passed from the sub-domain to the parent domain, however, to a far lesser extent.
For this reason, while sub-domains have their place and value, it is always far better to populate a parent domain with content along with any sub-domain.
You have two things to consider if you want to move your content from the sub-domain to the parent domain. One is any existing links and what value these links may have. The other is the cost of moving your content from the sub-domain to the parent domain. Both can be dealt with.
Let's assume your decision is made and you do want to move your content. What needs to happen?
You need to move your content and deal with any links. If the links are of little to no value, then it may be better/easier to forget them and delete the sub-domain. However, if these links have value that you want, then you can in theory retain your sub-domain and simply do a blanket redirect from your sub-domain to your parent domain.
There is an easier way to move your content within Apache. If you are using a CMS of some sort, then you will have to do some configuration changes to reflect the URL change.
In Apache, there are two basic configurations, old and new. Some installs still use the older style configuration /etc/apache2/httpd.conf while others use /etc/apache2/sites-available/000-default.conf or example.com.conf and sub-domain.example.com.conf. Whichever applies, you will open the file and find the DocumentRoot and Directory directives for the parent domain and simply change it to use the directory for the sub-domain. For the sub-domain, you will edit these same values to point to a newly created directory where you will place an .htaccess file with a blanket redirect to the parent domain.
This is usually a simple process but does require some care especially if you are new to Apache.
Anytime sites are changed to this level, Google and the other search engines will need to reindex the sub-domain and parent domain. This takes a while. In fact, depending on the freshness metric for each site, it can take quite a while. But it is well worth the effort and patience.
Why? Because you will be adding value to the parent domain that should have existed all along. If you chose to use the sub-domain for something else, the sub-domain will perform better as well as the parent domain in the long-run.