Cats can willingly starve themselves to death or become anorectic. It is not true that they will eventually swap to eating whatever you're offering, if they are suitably stressed out.
Please keep an eye on how your kitty eats, how often and if they are retaining weight or losing it. If your kitty starts horking up stomach fluids/stomach fluids with foam/stomach fluids with bile, but there's no sign of hairballs or food, take the kitty to the vet.
At least it was caught early enough with Didi and she's currently getting some super-boosted high-energy food, fresh meat and appetite-boosting medication (original use: human antidepressant