Kim Richards -- Homeless, Living Out of Car At Time of Arrest

Kim Richards was living out of her car when she was arrested Sunday for shoplifting at Target ... TMZ has learned.

Sources connected to the family tell us, Kim had been house-hopping since leaving rehab last month. She quickly ran out of friends and relatives who would extend themselves, and has been homeless ever since.

We're told Kim has been "self-medicating" recently, and although it's unclear if she was under the influence when she allegedly stole $600 worth of goods from Target, her conduct was truly bizarre. One law enforcement source says she left the store with more than 50 items in her shopping cart.

Kim's family does not know what to do ... they want to help but it's unclear at this point what can be done to help Kim.