well during the sequence where you go to the slave trader if you click the top option and the top option you will just go to him buy her (just select yes option) = family if you go no, yes, ... , thats exciting, nobody, don't free her, follow your brain you will leave without buying her and change your mind, after that ther eare few bits and bobs (wait for 2 days and go to the market) you will go back with taliya to the underground where you will find her demonized, which then unlocks the romance route, basically saving her with scarlet (+ scarlets home in the market).
If you do no, yes, ..., thats exciting, nobody, don't free her, follow the sensation - you buy her and she becomes your slave
EDIT: you made me actually load my files so i give you proper directions lmao.