Can a Homeowners Association (HOA) foreclose and if so can they kick me out?

An HOA can foreclose for past due amounts. If the property goes back to the HOA at trustee sale they would have the legal right to evict the occupants and sell or rent the property. HOA liens are typically junior to any Deeds of Trust so the HOA would be responsible for the payoff of any senior liens or loans or they could risk losing their ownership when if the senior Deed of Trust later foreclosed. Note that in California the homeowner does have a 90 day period during which they can redeem their ownership by paying the outstanding dues.