Act on this immediately, because furlough requests take time to process and time may be the one thing you do not have. Contact the facility and ask to speak with your husband's counselor or case manager today. Explain the situation plainly: his brother is on hospice, his condition is serious, and you are requesting a compassionate furlough for a family visit.
Furloughs are not granted freely. The standard criteria are that the inmate has a clean disciplinary record and is reasonably close to the end of their sentence. A spotless conduct history is essentially required. If your husband has any recent write-ups or incidents, that will significantly complicate the request, though a compassionate circumstance like an imminently dying sibling can sometimes carry weight even in cases that would not otherwise qualify.
Documentation matters. Have a letter from the hospice provider or treating physician that clearly states the terminal diagnosis and that time is limited. Submit that with the furlough request rather than just making a verbal ask. Written documentation creates a formal record and signals to the facility that this is a genuine medical emergency, not a general request for outside time.
If the counselor or case manager says he does not qualify, ask what options exist. Sometimes, a supervised visit at the facility, or in rare cases a brief escorted visit to the family member's location, is an alternative when a traditional furlough cannot be approved.
Do not wait. The request process takes time and the window may be short.