Below is a complete listing of current preferred stocks of Real Estate Investment Trusts (REITs). With Banks REITS of the largest issuers of preferred stocks and some of them finance their businesses entirely with preferred and common stock issuance and avoid debt–Public Storage and PS Business Parks are the 2 that finance their businesses with preferred issuances. You can see below that both have many preferred stock issues outstanding.
Preferred stocks of REITs do NOT pay qualified dividends. Dividends are cumulative in all cases.