In some cases, spouses and other family members are allowed to use a VA-eligible predecessor's eligibility. The VA says that in most cases, the death must be service-related, and the spouse can not have remarried. Here are the terms, per the VA:
"You are an un-remarried spouse of a Veteran who died while in service or from a service-connected disability
You are a spouse of a Servicemember missing in action or a prisoner of war
You are a surviving spouse in receipt of Dependency and Indemnity Compensation (DIC) benefits in cases where the Veteran's death was not service-connected
A surviving spouse who remarries on or after age 57 and on or after December 16, 2003, may be eligible for the home loan benefit. However, a surviving spouse who remarried before December 16, 2003, and on or after age 57, must have applied no later than December 15, 2004, to establish eligibility."
Good luck and thank you for writing.