According to Donation Town, there are charities that provide free washers and dryers to consumers that are in need. However, the exact requirements for receiving a free washer and dryer, as well as the availability of any free products, vary based on a person's location.
In most cases, washers and dryers that are given to consumers in need have been donated either by an individual or a corporation. However, Donation Town also states that these donations may be sold by a receiving charity in order to fund activities or additional services. So while someone in need may not receive a completely free washer and dryer, he may be able to purchase one at a discounted rate through the charity.
Wealth Informatics discusses another option for free washers and dryers, the Low-Income Home Energy Assistance Program, or LIHEAP. This program is funded by the federal government and is focused on consumers who are at or below a certain percentage of the federal poverty level. The exact requirements for LIHEAP vary by state; the application process also varies by state. LIHEAP may also provide assistance with utility payments and appliance installation, and it can provide assistance with obtaining heaters and air conditioners.