But it won't though and here is why:

  The issuer of the stable coin needs to collect $1 USD to issue $1 in stable coins.  They keep that dollar in the bank.  If the FIAT system wasn't a corrupt bunch of bullshit that additional demand and holding would help perpetuate the USD.  But FIAT is a corrupt bunch of bullshit so when they put that $1 in the bank the bank lends out .95.  So there is no actual holding of those dollars because the bank doesn't have your money or theirs.  They just loan it right back out actual creating more dollars in the process.