"Ran out" as in the amount they harvest runs out since the simulation kind of looks like the rings are destroyed meaning no new source of particles
It's difficult to see what your point is here. If the particles have a limited duration, then the environment of the ring planet's system would have been replenishing them in some fashion. Therefor if the particle you have lose effectiveness in time, you simply return to the original source, and get more.
However, if the particle's emissions are perpetual, then the Federation's particles will never "run out."
Remember Hartzilla, the particles didn't run out while in orbit of the ring planet, the last thing anybody would want to do is change the particle's emissions in the process of the harvest. So the particles in orbit, are the particles after harvest.
Again in the simulation it looked like THE. RINGS. WERE. DISINTEGRATING.
As in no more rings, as in no more radiation being generated. If there are no new particles being generated because THERE ARE NO RINGS TO GENERATE THEM then that means there is only a limited supply that will eventually run out.