Local Buy Nothing Groups exist for two purposes. They help people clear out their homes of items they no longer need, without the hassle of going to a donation center or the dump. And they also connect those people with others who may need those items. If you have someone in your neighborhood who's renovating their home or clearing out a garage, there's a chance they could be giving away a fridge for free.
NextDoor is a great neighborhood resource for digitally eavesdropping on nosy neighbors and finding items in your community. You could create a post with the appliances that you're in need of, whether that's a fridge, a microwave, or even a washer/dryer.
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