It appears to me that QE has been employed after the collapse of housing bubbles - both in Japan in the early nineties and in many other countries around 2008. During a housing bubble there is a high rate of borrowing and when the bubble collapses the rate of borrowing will reduce dramatically and so (in the absence of any central bank intervention) the money supply will start to fall as existing mortgage principal repayments extinguish previously lent out credit... I once saw a video of the former governor of the Bank of England say words to the effect that QE was being used to compensate for this fall but the publishing of this notion seems to be rare as hens teeth. I have never come across an article that concurs with this idea. Indeed you can read many many descriptions of QE (including Wikipedia) that make no mention whatsoever of the idea of money being extinguished by the repayment of loans or that the money supply might fall without QE.
So either:
- I have just been reading the wrong articles
or
- QE is unrelated to any potential fall in the money supply in the absence of intervention