"Raj goes to her home."
Translation:राज उसके घर जाता है।
Sure. This has come up a few times for different sentences, and is definitely very subtle: so basically the sentence could also be written as 'राज उसके घर को जाता है' (Raj goes TO her home). The को is often omitted in sentences like this, but the fact that the action is happening TO the subject (घर) remains the case. Anytime a word is modifying the object (घर में, घर के सामने, घर का कमरा, etc.) you have to use the oblique form, even when the word isn't explicitly written (which is the case here). So it's still उसके. I've heard this called a 'ghostposition', which is pretty apt!