Do backlinks pointing to the main domain increase SERP for the sub-domains?

Do backlinks pointing to the main domain increase SERP for the sub-domains?

Some people use sub-domains for different parts of their website. For example, they will use forum.yourdomain.com for their forum and blog.yourdomain.com for their blog. Most of the time when they create backlinks, it will link to the root domain yourdomain.com. My question is, do backlinks pointing to the main domain increase SERP for the sub-domains?

I have two different thoughts here. Firstly, I have seen lots of people use sub-domains for different parts of their website. A good example is Digital Point. As far as I know, websites like these don’t create backlinks for each of their different sub-domains. That suggests that it does increase SERP for its sub-domains. Another thought is that, lots of hosts provide sub-domains for their clients but this time, the backlinks to the main site won’t benefit the sub domains. This suggests that it doesn't increase SERP for its sub-domains.