If prices go back down, it’s Deflation the opposite of Inflation.
Inflation “cooling down” is not the opposite of Inflation, it’s merely less of it, or in other words prices going up but not as fast as before.
If people are crushed by the rise in living cost from previous high Inflation, less Inflation by itself will do nothing at all to solve their problem and in fact it will crush them some more, it’s just that the increase in crushing won’t be as fast as with higher Inflation.
There are only two ways of them to be less crushed: either Deflation (i.e. prices actually go down) or their incomes increase (which for most people means their salaries go up).