Obviously, it's now an essentially inert artifact not going anywhere under its own thrust. The perihelion of 67P is about 20% larger than Earth's aphelion. Assuming its orbit is stable, neither the comet nor any debris or human artifact it may shed could be expected to come anywhere near Earth. But, is its orbit stable? If not, in what way is it changing? Would it get closer to Earth in the future - perhaps centuries or millenia from now?
I used the JPL Horizons database and downloaded the predicted positions (state vectors) of Earth and Comet 67P at 10 day intervals from 1600-Jan-01 to 2500-Dec-01.
edit: As @pericynthion pointed out in comments, since comets are subject to various non-gravitational forces, including "propulsion" by gasses vented unevenly and unpredictably by the rotating (and potentially wobbly) comet, long term predictions are not necessarily as reliable as they would be for far more massive planets. I'll see what I can to do find out more about this particular ephemeris for this particularly well-characterized comet that never gets closer than 1.2 AU from the sun (within this prediction).
In the case of the ephemeris I've used here, the three Marsden non-gravitational force parameters $A_1, A_2, A_3$ are shown and presumably are active. This is an empirical way to try to parameterize and approximate all of the forces besides gravity that affect a comet's orbit.
Here are the results. I'm not sure this answers your question yet. It's a good question - why there are a series of closer approaches between the years 1950 and 2200, and the answer is what it usually is - Jupiter! A close approach around 1959 bumps it into an orbit that occasionally gets ear earth, and later another close approach around 2209 bumps it out again. That darn Jupiter, always keeping things interesting!