I caution the class to do a lot of serious research and if possible talk to people who already have fiber animals like sheep, angora bunnies, goats, alpacas, and/or llamas. Norwegian Forest Cats and Symoyand dogs can also provide a lot of fiber, with Forest Cat does better with 25 percent wool but you can still buy pounds of that from wool outlets and card it up with the soft under-coat of the cats.
Samoyed fur can be spun and used as is, but as I learned from a professional, it can be too warm - for example, she only made vests, she got feedback that sweaters with sleeves got too warm even in Alaskan Winters (she was based in Colorado). But you could make a cape/blanket to pin on and take off if someone was overheating.
We had sheep our first few years here and while it can work for some people, we found the problems of fence jumping and a lack of shearers to be severe problems. When foot and mouth hit years ago I was in the hospital facing emergency surgery the next day and the cops called and said we had overnight to hunt the escapees down and shoot them or be fined 100,000 pounds! My husband and his former cop buddy from the US went home and went sheep hunting.
We then tried rabbits and have never managed to keep them alive very long, if things get seriously bad again I will try "Operation Rabbit" part 10 or 12, but with 18 cats and a lot of foxes and sometimes dogs - keeping everything secure is difficult. Also, fiber rabbits don't make good meat rabbits and vice versa, so you need to keep me than one strain if you goal if both fiber and food.
Now people with the right set up for a few sheep - good fencing, the right land, knowing all the right skills can do llamas or alpacas pretty easily at least one or two at a time. They will live with the sheep and fight out predators including stray dogs and coyotes.
In some areas look at nettle fibers (they are everywhere here), flax and even cotton may be alternatives though all are labor-intensive and you need to ret (rot) the nettle or flax which can get messy but many frontier homes in the US and cottages in Ireland had "retting ponds" for just this purpose.
My actual advice to the class is to get as much fiber and already made yarn NOW, while you still can without breaking the bank and storing it in big plastic tubs or other moth-proof areas. Sock Yarn which is usually 75 percent wool can still be pretty cheap and is useful for a lot of things besides just socks (including washable children's and baby clothing).
While I prefer to work in 100 percent wool yarns, the more common (and cheaper) 80 wool/20 polyester and even some of the 20 wool/80 polyester are better than nothing and very useful for some items like Fall/Spring Sweaters, blankets, children's clothing, Fall/Spring hats, etc.
Cotton yarns are useful for many items as well and are often on sale, at least over here - the problems are the factories in China are not shipping anymore (or in some cases producing) so the stocks may be limited.
Finally, polyester/man-made fiber yarns can be useful for some things like hot-water bottle covers, some baby clothing, bags for shopping (or gathering apples), knitting practice, cat toys, children's soft toys, and even adult clothing in a pinch though it will tend to stretch, pill and not be nearly as warm as wool.
If this is all the yarn you can get now, at least get some and practice, you can also use it along with wool (use two strands together) to make a warm but stronger fiber, which will be warm.
So, I'm not saying don't get fiber animals, this is the BEST LONG-TERM solution for those who can manage it and/or setting up trade relationships with a neighbor now (probably using cash at this point) so that if things go to pieces you have contacts you can barter or buy wool/other fibers from.
But again, I suggest first getting some well-prepared, commercial spinning wool, a set of carding combs, a drop spindle, and start to practice before getting supper invested.
I won't even get started on weaving in this post, but that's another useful prepping skill but I suspect it will come into play a bit later in a real collapse situation, as clothing and fabric run out and people realize the limits of knitting.
Everyone in a family who is able-bodied and over about six years of age can learn to knit, small loom weaving is the same way, but for production weaving, you need a full-sized loom and set up. A good investment for many families after sorting other things out and/or if someone already has a serious interest in it.