so you've witnessed chimney fires and lived to tell about it? did the house(s) burn down? but to answer your question, starve the fire for oxygen. can't have a fire without oxygen. step 2, garden hose. step 3 fire department. step 4 consult a mortician. . . so I answered your question. can you define this part of your text? I'm looking for a length of time. for example; a day, a week, a year? cause "over time" no chimney will last.Maybe you could explain the proper way to control a chimney fire.
Because there was no controlling the ones I've been witness to, they burned full speed ahead until burned out even with things shut off down below. Makes for quite a show...
Over time - and not much time in cases - one can crack your liner in short order.