I have slept with decks tucked under the pillow, inside the pillowslip, for several reasons.
I do this to season a new deck or condition a pre-owned one. Five nights straight seems to do it. With my pre-owned Tarot for Cats, I definitely felt the energy of the previous owner releasing from the cards when I started the first night. Not an unpleasant thing, for the previous owner seemed very nice. In deck conditioning, each night I focus on a suit energy, starting with Earth which is my base energy as a Capricorn. On the last night I focus on integrating the four suits, which analogous to the meaning of the Majors.
Also, for Legend: The Arthurian Tarot I have just finished working through the 78 cards, one card per night. I used the order the deck came in, starting with the Majors. I would study the card, read the explanation and story in companion book, A Keeper of Words, and then go to sleep on it. I put the current card at the top of the whole deck - I did not want to sleep with one card by itself since I thought I would bend it.
This discipline was not consciously planned. I was originally thinking of seasoning the deck, but I also wanted to start studying the cards and doing so at the end of the day seemed to be an opportune time. But when I put the last moment study and the cards under the pillow together, I was treated to two beautiful dreams on the Fool, and another wonderful dream on the High Priestess. So I realized that the unconscious was inviting me to continue with this dream programming throughout the deck. I did not always have remembered dreams, but I didn't worry about it. I felt that the dream world would only comment if there was something significant to say.
When the 78 nights ended last week, there were two unpleasant nights when the dream world seemed to miss the guidance of dream programming, and I spent these nights in chaotic dreams and broken sleep. I had started on a new deck right away, studying a card just before sleep, but without putting the deck under my pillow. Without the deck under the pillow there was no detectable response in dreamtime.