The Protecting Elders From Government Error Act limits how Social Security can recover overpayments from beneficiaries when the government is at fault. The bill prevents the Social Security Administration from recovering overpayments to elderly retirees if more than six months have passed since the overpayment occurred and the error was the government's mistake, and it caps monthly benefit withholding for government-caused overpayments at five percent of the monthly benefit amount. These protections do not apply if the beneficiary committed fraud or similar misconduct. The bill takes effect immediately upon enactment and applies to all outstanding overpayments dating back to when the law is signed, affecting current and future Social Security recipients who have received more than they were entitled to due to administrative errors.