The article provides a description of heretofore neglected Finnish converb clauses, in which the passive simultaneous converb in -taessa/-täessä ‘when V-ed; while being V-ed’ is followed by a possessive suffix, most often the third-person possessive suffix -Vn. Based on data drawn from a body of modern written Finnish, and accompanied by the results obtained from a questionnaire survey with native speakers, the article claims that person-marked passive converb forms like lausuttaessaan ‘when uttered’ and perustettaessaan ‘when established’ need not be considered downright erroneous contaminations by L2 learners or careless L1 writers. Instead, they are widely accepted in sentences where the possessive suffix refers to the patient of a transitive verb in the passive converb form, identical with the non-agentive theme argument of the main clause, as in Varasto oli perustettaessaan Euroopan suurin [storage be.pst.3sg establish.pass.cvb.3 Europe.gen large.sup] ‘When established, the storage was the largest one in Europe’.