They have assurance (as I assume all Christian believers do) because their salvation is based on the finished work of Jesus Christ. The assurance comes from the scriptures. For example, Hebrews 6.17-20:
17 Thus God, determining to show more abundantly to the heirs of promise the immutability of His counsel, confirmed it by an oath,
18 that by two immutable things, in which it is impossible for God to lie, we might have strong consolation, who have fled for refuge to lay hold of the hope set before us.
19 This hope we have as an anchor of the soul, both sure and steadfast, and which enters the Presence behind the veil,
20 where the forerunner has entered for us, even Jesus, having become High Priest forever according to the order of Melchizedek.
The assurance is confirmed by the work of the Holy Spirit. Romans 8.16-17:
16 The Spirit itself beareth witness with our spirit, that we are the children of God:
17 ¶ And if children, then heirs; heirs of God, and joint–heirs with Christ; if so be that we suffer with him, that we may be also glorified together.