Is it permissible to walk with socks over a dry place that was previously defiled with urine and not washed, then pray with these same socks, knowing that the walking was accidental?

If the impurity dries and no moisture remains in it, it does not transfer to a dry object that touches it. Therefore, a person's foot or dry sock does not become impure by walking over a dry impure spot, and their prayer with those socks is valid. Nevertheless, one should avoid walking over impurities because the Sharia has commanded guarding against impurities, and there might be a slight imperceptible moisture present.