It's not a good idea, but my very frugal mother did it. BTW, I don't even try to unwind them, I take an exacto knife to the whole mess.
I was taught to be very frugal with thread. My mother was of the Depression generation, raised by a mother who was the sole support of the family, (with a disabled husband). "Extra" thread was put aside for hand sewing. I buy most of my thread on large cones. Adjusting for inflation, my thread is much cheaper than theirs.
Remember, torn shirts became rags, or rugs. even very small scraps of fabric became quilts. don't judge these people harshly.