If I have a HELOC and my house is forclosed upon, what is my responsibility in a non-deficiency state?

You are correct that Arizona protects homeowners through a pair of "anti-deficiiency statutes."  These laws protect homeowners who lose their homes through foreclosure from having to pay the deficiency between the amount owed and the amount realized from the sale of the property.  However, the relevant statute, ARS 33-729(A) only applies to "purchase money mortgages,"  that is mortgages taken out to fund the original purchase of the home.