What Happens to the House That Secures a Reverse Mortgage? My answer to this question applies to the HECM program administered by HUD, with investors in the mortgages insured against loss by the Federal Housing Administration (FHA). Newer:Home Insurance 101: The Fundamentals of Home QualityOlder:The Importance of Choosing the Right Mortgage Broker PostedNovember 2, 2016 AuthorDante Royster