How to React to Being Dumped

An ex once explained to Natalia that in Britain, one would be well advised not to apologise to the other party following a car accident. She declined the offer of assistance. What she's asking us is how should you react to being dumped? Is it best to be dignified and not show your feelings? Or should she have let her feelings out the next time? And let the ungrateful opposite party know how she feels. Can you ever be friends with the wrecks?