If you were to buy a brand of pet food that your pet won't eat for whatever reason. Don't toss it out in the trash, look in your phonebook to see if your city/town has a no kill animal shelter.
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Animal shelters will welcome towels, sheets, blankets, pillows, and any other linens that are too worn-out to be given to someone else. Do a good deed for animals and save our planet as well.
Many animal shelters and veterinarians will take your old blankets and towels to use for their animal bedding. Just make sure it is clean and you have given a gift that many animals will enjoy for a long time.
You may be thinking about spring cleaning, and tossing towels and sheets that have seen better days. Take them to your local shelter.
I have done volunteer work for the SPCA in my younger years. Many little lost or surrendered animals are scared, sick, or hurt. They do not understand being in a cage and being around all of the animals that are barking. These animal shelters will take blankets, stuffed animals, etc.