Unfortunately there are no benefits that would continue after your Father-in-Law passes. However, you may apply for the VA Veterans Pension for your Father-in-Law and his son may qualify as a dependent. You should speak to a local veterans service officer in your area to see if there are any state benefits that may be able to assist.
Based upon the assets of the father, you may need to look into the creation of a Special Needs Trust for the disabled son. This could enable him to receive benefits without being denied due to an inheritance. Please speak with an Elder Law attorney.