My character is sleeping. While sleeping he turns around but the blanket on him doesn't move. 

How to fix it? 

Can you provide more details? Is the blanket soft cloth?
Assuming the blanket is soft cloth, where have you pinned it (if anywhere)?
If the blanket is soft cloth and it is pinned then you will need to unpin it so that it can move.
If the blanket is soft cloth but is not pinned then you can try one of a couple things:
1. Adjust the character collision area so that more of the character collides with the blanket.
2. Adjust the friction value on the blanket to try to increase the interaction between the character and blanket.
3. Fake it: Pin the blanket to a dummy object (an object not seen in the final render) and use it to control (pull) the blanket.

"We often compare ourselves to the U.S. and often they come out the best, but they only have the right to bear arms while we have the right to bare breasts"
Bowser and Blue, Busting The Breast