Disabled Homestead Exemption

[VanAnthony Williams]

Hello,

My future father-in-law has decided he is exempt from paying his taxes because of his disabled status. I believe his status only exempts him from being removed from his property because of delinquent taxes, but he doesn't forgive his tax responsibility. I've been talking to my fiance and her siblings about the fact that they may be hit with a tax bill when he passes or lose the property outright. 

Am I correct in my assumption that this burden will just be passed down to whoever inherits the property, or will the taxes be forgiven with his passing?