As a speaker of British English I am not at all sure what a 'closet' is, let alone a 'bottom closet'. (I know what a water closet is, and what is meant by coming out of the closet, but that's it)
Is this what I would call the 'bottom drawer' of a 'chest of drawers' ?
Or are there two 'cupboards' here, one on top of the other ?
If you're not going to use closet, dresser, armoire or wardrobe works better for linens and clothing. (Unless you actually keep them in an actual cabinet - like a kitchen, bathroom or filling cabinet).
No one uses cabinet for sheets or clothing, unless they're in a tiny studio apartment, and prone to using their oven for book storage, because they have so little space. Then sure, the blanket might be next to your cereal and coffee in the cabinet.
(The exception to this being medical usage - Search blanket warmer cabinet).