DY, what do you mean by muktzeh?
LU was worried that carrying around her bag of tissues was a problem because the tissues are muktzeh and therefore the bag as well (bosis).
But what if the tissues have already been used 10 times?
At the point where all of the tissues are shredded being any possibility of further use even an emergency, if there are no other tissues in the bag, you might want to go to the nearest trash can (although we could still find you a heter).