It's not just the one who was dumped who has it tough. Deciding to leave someone is a horrible decision to have to make and it's never made lightly. It requires a lot of thought and courage. At the end of the day, no-one likes to see someone else suffer, let alone someone they have loved and probably still do in a way.
This is why the one to do the dumping can be plagued with guilt. It shows their compassion, and you shouldn't reject it - but you shouldn't encourage either. The decision has been taken and there's a reason why, whatever it is (you were going nowhere, you didn't both feel the same way, you got stuck in a rut and wore each other down...we could go on!).
Remember too that sometimes, when you have a lot of respect and affection for someone, it's easier to stay than it is to leave. But this equals one person's sacrifice for another's comfort, and obviously it'll never work. It's more of an arrangement between two people than a relationship, and in the end nobody wins.
The final stage in the healing process for some women is finding compassion and understanding for their ex. Normally at this stage you can bring yourself to see him socially again and hopefully stay on good terms.