The only thing that comes to mind is cotton batting that is used when making quilts. I’m unsure how it would hold up. Probably better that the one I’m using currently. I’ve never used one before but purchased a small one for some new squash I’m growing. It does not like the wind! Not at all.
Depends on what you need exactly, but I use sheep wool a lot. It's great as mulch, but can't be a top layer. I use raw dirty wool in the garden for covering stuff, and I will use it soon under a pond, and I knit simple blankets which I will use in the garden when they wear out.
I guess knitting a blanket just to use it in the garden might be too much work, but it's certainly doable too... you can also use old clothes of course, but they usually contain some % of plastic.
I found sheep's wool is good as a general mulcher. Some grasses get through, but little and I'm overall very pleased with it, although I dono if I'd use it as a replacement for garden fleece which helps the plants underneath it grow
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