The theme I gather from this Psalm is one of forgiveness, grace, and love of a God so great that He will always welcome us back if we yield to Him.
6 We have sinned, even as our ancestors did;
we have done wrong and acted wickedly.
7 When our ancestors were in Egypt,
they gave no thought to your miracles;
they did not remember your many kindnesses,
and they rebelled by the sea, the Red Sea.[b]
8 Yet he saved them for his name’s sake,
to make his mighty power known.
9 He rebuked the Red Sea, and it dried up;
he led them through the depths as through a desert.
10 He saved them from the hand of the foe;
from the hand of the enemy he redeemed them.
11 The waters covered their adversaries;
not one of them survived.
12 Then they believed his promises
and sang his praise.
we have done wrong and acted wickedly.
7 When our ancestors were in Egypt,
they gave no thought to your miracles;
they did not remember your many kindnesses,
and they rebelled by the sea, the Red Sea.[b]
8 Yet he saved them for his name’s sake,
to make his mighty power known.
9 He rebuked the Red Sea, and it dried up;
he led them through the depths as through a desert.
10 He saved them from the hand of the foe;
from the hand of the enemy he redeemed them.
11 The waters covered their adversaries;
not one of them survived.
12 Then they believed his promises
and sang his praise.
...
40 Therefore the Lord was angry with his people
and abhorred his inheritance.
41 He gave them into the hands of the nations,
and their foes ruled over them.
42 Their enemies oppressed them
and subjected them to their power.
43 Many times he delivered them,
but they were bent on rebellion
and they wasted away in their sin.
44 Yet he took note of their distress
when he heard their cry;
45 for their sake he remembered his covenant
and out of his great love he relented.
46 He caused all who held them captive
to show them mercy.
and abhorred his inheritance.
41 He gave them into the hands of the nations,
and their foes ruled over them.
42 Their enemies oppressed them
and subjected them to their power.
43 Many times he delivered them,
but they were bent on rebellion
and they wasted away in their sin.
44 Yet he took note of their distress
when he heard their cry;
45 for their sake he remembered his covenant
and out of his great love he relented.
46 He caused all who held them captive
to show them mercy.
...
As well we have the parables of the Prodigal Son from Luke 15:11-32 and of the Lost Sheep from Luke 15:1-7.