I've got a Yellow Jacket target that I've had for probably 10 years. I replace the cover every year or two...needs it again. The insides seem to be made mostly of bits of cloth and the stuff my wife uses for quilt batting. It stops the arrows well and the stuff doesn't pull out very much. I may have to do a major overhaul the next time because the stuffing in the center has migrated outwards pretty badly, but I think it will be doable. As far as bag targets go, these are VERY durable.
I bought some Hurricane bags because they were cheap. I soon found out why. They were stuffed with what looked to be scraps of seat cover material...cloth bonded to about 1/4" thick foam rubber. The stuffing grabs on to arrows and refuses to let go, so you end up pulling large chunks of it out through what soon becomes a large hole in the target. Durability absolutely sucks!
If I were doing DIY bags, I'd do what nek4me suggested, but I'd probably use cloth on the inside for the most part. Go to Goodwill and buy up a bunch of cheap cotton stuff that nobody wants, cut it up a bit and stuff the bag. Depending on your arrow speed/construction, friction can make some of the synthetic stuff kind of melt around your arrow at do about what the foam rubber crap in the Hurricane bags does. DON'T use foam rubber!