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$PUSD is the stablecoin which protocol borrowers can collaterize the $BNB and borrow $PUSD.
How does $PUSD closely follow the price of USD?
The ability to redeem $PUSD for $BNB at face value (i.e. 1 $PUSD for $1 of $BNB) and the minimum collateral ratio of 110% create a price floor and price ceiling (respectively) through arbitrage opportunities. We call these "hard peg mechanisms" since they are based on direct processes.
$PUSD also benefits from less direct mechanisms for USD parity — called "soft peg mechanisms". One of these mechanisms is parity as a Schelling point. Since Piggy treats $PUSD as being equal to USD, parity between the two is an implied equilibrium state of the protocol. Another of these mechanisms is the borrowing fee on new debts. As redemptions increase (implying $PUSD is below $1), so too does the baserate — making borrowing less attractive which keeps new $PUSD from hitting the market and driving the price below $1.