Link building is a field with as many strategies as people can conceive. While the methods employed may be different for each campaign, the ultimate goal is the same: to receive enough authority to rank high in search engine results. One such method that is white hat, legitimate and ultimately helps other websites is called broken link building.
Beyond finding broken links and contacting webmasters, the person undertaking this strategy has to ensure they have content that webmasters want to link to. The best way to ensure that said content is suitable is by using any variety of rebuilding tools to see what the defunct websites had on those pages.