This is the 3284th most frequent Russian word.
останутся
"Останутся" means "will remain" or "will stay."
Here, 'останутся' implies a condition where no tickets will be available because they have already been sold; it's about the state of being sold.
Если мы не поторопимся, билеты останутся проданы.
If we don't hurry, the tickets will remain sold.
In this sentence, 'останутся' refers to memories that will persist or stay with us emotionally.
Многие воспоминания останутся в нашем сердце.
Many memories will remain in our hearts.
The word 'останутся' is used to indicate that the books will not be moved from the table and will stay there in the future.