Rental Assistance Housing Preservation and Rehabilitation Act of 2014 - Modifies funding requirements for the Rental Assistance Demonstration, provided in the Department of Housing and Urban Development Appropriations Act, 2012, for voluntary conversion of properties assisted via public housing agencies from the Public Housing Capital and Operating Funds, or assisted under the moderate rehabilitation program to properties with assistance under a project-based subsidy contract or the voucher program.

Increases from 60,000 to 150,000 the maximum number of units currently receiving specified assistance required to be so converted.

Extends through FY2016 the eligibility for the conversion of assistance of owners of certain assisted properties for which an event after October 1, 2006 has caused or results in the termination of rental assistance or affordability restrictions and the issuance of tenant protection vouchers.