Are you sure there's no link behind? -- Most often, links are the major influence in any SERP ranking, and there has got to be some form of links that would help the site rank.
These days, perhaps even if that site is an expired domain, the expired domains do have old links, and most likely from extremely high PA/DA sites that has in excess of 80-90 DA/PA, and if the tool showed no new links built, then I'm sure the old links are playing the SERP ranking, as it is indeed contributing authority to that site.