If all the people in the US start to save their money, their bank accounts grow. But the goods are being imported and therefore if USD falls these goods will be more expansive to buy thus for importers to make money they have to sell for more or take a hit. So your goods aren't going down are they. If the FED keeps buying US debt and thus they print more paper eventually that paper flows into the system thus supporting the goods if not increasing them even though people aren't buying. What that creates is a stagflation with a risk of your saving account having more money which is buying less goods.
East Europe is prime example of that. People could try to save but the inflation ate up their savings faster than they could save. Inflation was not created but people buying more goods and pushing the prices higher but by the dilution of the currency. US seems to have the same problem today. By being indebted and has exported so much of their manufacturing they may need to keep those presses running full tilt to absorb the repayment of debt which only creates more problems and inflation is one of those.
Just because the FED helps financial institutions doesn't mean the FED will help Joe Sixpack.