Shell companies are lawful and common. They are used for holding structures, joint ventures, securitisation and dormant name protection. What makes them relevant here is that an entity with no operations leaves almost no evidence about who really controls it, so a chain of them is an effective way to put distance between an asset and its owner.
The signals investigators use are consequently indirect: incorporation immediately before a transaction, registered addresses shared with hundreds of unrelated entities, filings that stay dormant while large sums move, and directors who appear on implausible numbers of unrelated boards.