Theft Rate of Linen and Towels

No - we dont have much problem either. I would say maybe be lost 20% of our towels after 5 years of operation. Linen and blankets even less.
Our biggest loss due to theft has been a house guitar from the common room, and a few pots from the kitchen, and one hammock from outside.

Thinking of start putting them in the rotation and start handing them out to our guest. what's anyone think about that?

That's exactly what I did with towels that were left behind as long as they were in good shape. It worked out well for me. Every year our collection grew so I could afford to get rid of the ones that looked less presentable.

The biggest problem I had with towels was accidentally collecting guests' personal towels along with the hostel's stock from the laundry because they looked similar, especially the white ones. If we couldn't identify a guest's towel in the laundry, then I usually just invited them to pick their favorite from our collection to take with them.

This problem could probably be resolved by buying colored towels for the hostel, but that's no good if you have to replace your entire stock. I do NOT recommend embroidering any names or logos onto your towels to identify them though, because then they immediately become souvenirs and people want to take them home.

Theft rate of linen is approx. 10 % yearly, and it is very hard to control it, since guests do not like to be controlled at check-out and prefer to slip away from the hostel and not even report to reception.
Theft of blankets is rare, unless you buy some super comfortable sort (mostly women steal it).
As concerning towels, guests prefer to exchange their dirty towel with your clean one and leave, and even forget towels too - so you will probably have surplus of these.

Do you have electronic door lock controls to verify that no one else was in the room?

You're not likely to know if she actually stole it or just ditched it somewhere without looking in her bags (which you can't do). It's unlikely that she's going to come to you and point out that the pillow is gone if she stole it though, right? If it's just stained and hidden away somewhere, then the question is whether or not the damage was an accident. If it was, then I wouldn't charge her, even if she did try to hide it.