Many people who sought help under a federal program created to keep them from losing their homes are instead getting saddled with huge, unexpected bills. Thousands now face a stark choice: Go deeper into debt, or foreclosure. Lenders routinely approved short-term “trial” loan modifications that reduced payments for desperate borrowers under the umbrella of the Obama administration’s Home Affordable Modification Program. But lenders continued to count the mortgages as delinquent or in default.