There are no error correction methods defined a the base A429 layer. As you noticed, words with an incorrect parity bit are often simply ignored by a receiver.
At application level, additional logic usually takes place if a certain word has not been received for a sufficient amount of time. For example a flight control computer might assume that the angle of attack information is invalid if the AOA word has not been refreshed for X amount of milliseconds (either because of a parity error, or complete absence of the word on the bus).
However, there are ARINC protocols built on top of A429 that do have error recovery mechanisms.
For example ARINC-739 (which defines MCDU communication), defines an ACK/NAK mechanism so that the receiver system can ask the transmitting one to resend some information.
Similarly, Williamsburg protocol (also defined in A429) defines explicit ACK/NAK and retransmission in case of error.