[snrplfth]

Not how orbits work. A collision can't cause, for example, an object with a circular orbit at 400km (passive reentry regime) to become fragments with a circular orbit at, say, 2000km (non-passive reentry regime.) Like snaily said, all fragments originating from a collision will still pass through the point of collision, which, if it is still in the upper atmosphere, will lead to reentry. Orbital debris is actually very dissimilar to gas escape.

[kobeya]

Multiple collisions. Multiple.

[snrplfth]

The proportion of fragments that would have their orbits boosted, through multiple collisions, to an orbit higher than the upper atmosphere, is trivial. Nearly every angle of collision between two objects in orbit lowers their periapses. The risk of Kessler Syndrome doesn't come from objects in upper-atmosphere orbits somehow getting boosted out through collision chains, it comes from collisions between objects already in higher orbits not strongly affected by atmospheric drag (>600km).

[Snowdax]

It can me infinite collisions. It does not matter. Conservation of momentum still applies. The system of collisions only have a finite amount of energy. And it's chaotic rather than engineered. So it's not cumulative, much more likely to happen at numerous different angles cancelling previous collision trajectories out.