The Board of Immigration Appeals has determined that death threats constitute persecution if they are objectively credible and issued by a person or persons with the immediate ability to carry them out. The standard is seemingly in line with circuit court precedent, but the application of the standard is extreme. The Board found that receipt of an anonymous death threat accompanied by the delivery of bullets was not sufficiently credible or imminent.
The full text of Matter of E-M-F-S- can be found here: https://www.justice.gov/eoir/media/1422766/dl?inline