Time to buy.
One way it can go south is if Bitfinex is using the money it gets from Tethers to buy BTC. Effectively not converting the money to paper, but holding onto BTC. In other words, Tether may be backed by BTC.
So a run on Tether might affect the price of BTC negatively as Bitfinex would have to sell BTC to dollars to pay for the Tethers people are trying to sell back.
But that's only a theory.
In other words, it's like a bank you can only put money into, but not take money out of, and you can only redeem your money by finding some poor sucker who'll trade your USD vouchers for some other currency that's actually worth something.
Unless you're just talking about maintaining the peg by buying large amounts when the price falls below $1. In that case, yes they'd have to sell BTC to maintain the peg because it's conjectured that they back USDT with BTC (not USD), and even with the BTC they have, at its market value it wouldn't actually back the amount of Tethers they've printed.
That might be the case if Tether were actually backed by fiat.