Psalm 38:11 describes the isolation of a suffering man whose friends, companions, and relatives stand at a distance because of his affliction. In the psalm's immediate context, the suffering is intertwined with the psalmist's consciousness of personal sin, which distinguishes his situation in an important way from the sinless Christ.
Luke 23:49 records that Jesus' acquaintances and the women who followed Him stood at a distance watching the crucifixion. The visual correspondence is notable, but Luke does not cite Psalm 38:11 as prophecy. The connection should therefore be regarded as typological imagery rather than direct prediction. The experience of abandonment and distant friends expressed in the psalm is echoed at Calvary, while the New Testament maintains that Jesus Himself suffered without personal sin.