It happens to me at least once a year, or perhaps one in every several hundred pairs of tefillin I check. A parsha that just won't come out of the bayis. It is usually happens because someone very inconsiderate before me did not bother fitting the parsha properly into a suitable bayis and just forced the parsha (usually kadesh or vehaya im) letting it become the next guy's problem.
So while I have my tricks of the trade that I employ to remove stubborn parshiyos, sometimes they just don't budge. And once there is no matlis or saaros left and options are very limited.
My question is, what do you do when you go past the point of no return? ie the parsha may be damaged from your efforts to extract it, so you cannot just leave it there. Do you replace the bayis and parsha (putting the old ones in genizah) or do you continue trying to extract it even though in doing so you could ruin it further as well as possibly damage Hashem's name, but at least you save the bayis?