Can sankharas and craving arise without attachment?

I have noticed subtle thoughts (sankharas) can spontaneously pop up but mindfulness can quickly cut off & end those subtle thoughts so craving does not arise in relation to those thoughts. I have also noticed the mind via subtle craving can be drawn with some attraction towards an external sense object but mindfulness can quickly cut off & stop any attachment & becoming arising towards the sense object. Are there any Pali suttas that say the sankhara (2nd condition) and the craving (8th condition) referred to in Dependent Origination can arise without the further arising of attachment (9th condition), becoming (10th condition), birth (11th condition) and aging & death (12th condition)? Must every arising of ignorance, sankhara & tanha (craving) result in the Dependent Co-Arising of all twelve conditions of Dependent Origination?