My cat isn't sick and has been doing this for several years. She pees on only one rug when I put it in front of my kitchen door. Or if I put any towels on the floor in her room.
Cats do not like the noise or feel of aluminum foil when they walk on it and certainly will not pee on it, put it down where they usually "go" . As soon as they find this out they will go to the litter box as long as it is in a convenient place and clean.
When your cat pees on your clothing or bedding or towels it is trying to mingle its scent with yours. It is a complement, cat style. When she is targeting the rug in front of your front door, she may be smelling a neighborhood cat who has marked near your front door.
You might want to neuter your cat, if you haven't already. Make sure to wash all areas with an enzyme detergent that will remove all traces of smell. Your cat has marked its territory and will come back to the same spot.
My cat used to do this to any piece of clothing on the floor. It felt like she was doing it out of spite (because of the birth of my son) but she was probably just really confused.
Wish I had a solution for you, it's so frustrating when you can figure out why.
