[chmod775]

> In case of destruction, the satellite breaks up into many individual pieces each having a potentially very different orbit.

Depends on what you mean with "potentially very different orbit". Each piece still has to be at least on some elliptic orbit that eventually again passes through the spot where where it broke up*. If it was on a low orbit to begin with, it'll still burn up soon-ish as it decays. You cannot increase the perigee of some formerly circular orbit with only a singular application of force, nor can you increase the perigee of an elliptic orbit higher than its old apogee through the same means.

It'll take a lot to get pieces into orbits where they avoid decaying within a reasonable time span.

*Disregarding external factors like the gravitational pull of a third object, and assuming no drag and perfect point masses.