Is it true that if feet become impure with blood on a kitchen rug, it does not necessitate washing them due to hardship and the repeated occurrence of impurity, knowing that the rug will not be washed?

Continuing to ignore intrusive thoughts is the way to cure them. If a person who has stepped in blood enters with their shoes, the kitchen rug does not become impure if both the rug and the impurity are dry, for dry impurity does not transfer to dry. If there is doubt about the purity of the rug, its original state is purity. The foot does not become impure if it steps on an impure rug if both are dry, and doubt about the transfer of impurity does not render something impure. Furthermore, the prayer of one who prayed with an impurity unknowingly is valid according to some scholars.