How do we know that Christ's death applies to the elect?

In John 10:11, Jesus refers to Himself as the Good Shepherd who lays down His life for His sheep. This indicates that His atoning sacrifice is definite and directed towards the elect, as His death ensures that those represented by Him will be redeemed. The doctrine of limited atonement contends that Christ died specifically for those chosen by God, confirming that the elect will ultimately come to faith and be saved. As stated in Romans 8:33, the justification of the elect is assured since their sins have been fully borne by Christ.