Just speculating, so please jump in to confirm or discount...
(1) It could result in your site being indexed under the wrong domain/keyword(s). Or may be get indexed under both domains and then have issues with possible 'duplicate content'? Although I would have thought that search engines would be able to resolve such duplicate content OK in this case?
(2) They might be attempting to build up the ranking of their domain based on your content. At some later stage they might suddenly change their site for the 'real thing' and steal a lot of your traffic in the process?
(2a) Or they might be trying to build up the ranking of their domain in order to sell it for a higher price?