Hey Julien,
First of all, you have to understand that a stopped particle is different from a particle that stops sliding. Each particle is in a different state from the other.
If the particles are “stopped”, you can use a Group POP to group them with the Predefined Rules button (Particle is stopped) and in the Split POP, specify the group as the source group to split from.
If the particles slide to a stop, again with a Group POP, you can group them based on velocity or speed, which is an attribute.
There are two attributes you can use to find out which particles are newly birthed from another:
Generation Attribute (gen) and/or Origin Attribute (origin)
I used the Origin Attribute in my example hip file which you can download
here [pointy.tv]. I added comments to each POP so please read them to help you understand the setup better.
Of course, I hope my comments make sense.

Cheers!
steven