Why would it keep a minimum value? I don't think anyone will be supporting this token on purpose and making walls to stop it from collapsing, it an perfectly go to 0.
Tokens going to zero value means that no one has even the slightest hint of faith in them. That's not going to happen.
Someone will believe that the tokens will be ultimately redeemed for USD, at some price greater than zero. Just look at the altcoin market: for some reason there's lots of useless alts that won't go to zerothat's because there are some freaks out there that believe in them. Human diversity guarantees this.