At the time of Jesus, there were two main schools of thought on salvation: One was physical/superficial; the other was spiritual/deep.
The Sadducees say that there is no resurrection, and that there are neither angels nor spirits, but the Pharisees believe all these things.
If she believed superficially that there was no resurrection like the Sadducees, then she would interpret Jesus' words as preventing her from premature physical death.
Alternatively, she believed in the resurrection. I think this is the case. I'll explain my reasons.
First, there is depth to her emotions.
Luke 7:36 When one of the Pharisees invited Jesus to have dinner with him, he went to the Pharisee’s house and reclined at the table. 37A woman in that town who lived a sinful life learned that Jesus was eating at the Pharisee’s house, so she came there with an alabaster jar of perfume.
She recognized her sinful life and the power of Jesus. She came not an invited guest of the Pharisee. The act cost her dearly. The perfume was not cheap.
38 As she stood behind him at his feet weeping, she began to wet his feet with her tears. Then she wiped them with her hair, kissed them and poured perfume on them.
She kissed Jesus' feet with the utmost respect. She showed deep repentance.
Second, Jesus affirmed that her debt was deep.
41“Two people owed money to a certain moneylender. One owed him five hundred denarii, c and the other fifty. 42Neither of them had the money to pay him back, so he forgave the debts of both. Now which of them will love him more?”
43Simon replied, “I suppose the one who had the bigger debt forgiven.”
“You have judged correctly,” Jesus said.
Third, Jesus affirmed that her love was deep.
47Therefore, I tell you, her many sins have been forgiven—as her great love has shown. But whoever has been forgiven little loves little.”
Finally, Jesus' benediction was deep.
50 Jesus said to the woman, “Your faith has saved you; go in peace.”
Strong's Greek 1519: A primary preposition; to or into, of place, time, or purpose; also in adverbial phrases.
Go into peace as in
And the peace of God, which transcends all understanding, will guard your hearts and your minds in Christ Jesus.
Judging from the depth of her sins, her emotions, and her love, and the depth of Jesus' forgiveness and blessing, I'd argue that she understood her sins were forgiven and there was peace for her in the resurrection.