Can shredded paper be added to the soil to help loosen it?

Except for colored and glossy paper, which might contain some toxic heavy metals, newsprint and other paper is safe to use as mulch or in compost.

Here in the UK an old gardening hack is to put shredded newspaper (and peelings) directly into a trench in the vegetable garden and then in spring cover it with a layer of soil and plant our runner beans straight into it. I know that it's not really a direct answer to you question but thought you might be interested all the same :)

Yes, shredded paper can indeed be tilled or forked into the soil. Be aware some inks may not be the best for a veggie garden, but fine for a flower garden. We do shred all our envelopes, junk mail, everything for ours. This is especially helpful in hard clay soil or overly sandy soil.

I used it in my garden. It will keep the weeds down and bring on the earth worms, which are good for the soil.

Peat Moss worked into the soil works well too.

Shredded paper is great in compost - it is considered a "brown." Add some green and let it sit on top of the soil over the winter, then work into the soil in the spring. Or dig into the soil any time.