I think that Bullard makes a persuasive case that the amount of household wealth evaporated along with the crash in house prices should likely be viewed as a “permanent” (highly persistent) negative wealth shock. Standard theory (and common sense) suggests a corresponding permanent decline in consumer spending (with consumption growing along its original growth path). The implication is that the so-called “output gap” (the difference between actual and “trend” GDP) may be greatly overstated by conventional measures.
The final parenthetical here seems to me to embed an error. Don't think of the output gap as the gap between the actual and trend GDP; you call it an "output gap" because it's the gap between the country's output and its potential for output. It is entirely possible that a persistent wealth shock will lead to a corresponding permanent decline in consumer spending, but that shouldn't impact our potential for output. As an accounting identity, Consumption + Investment + Net Exports + Government Purchases = GDP. That means that if a wealth shock pushes C to a new lower trend path then either some combination of I + NX + G have to make up the gap or else GDP will decline to a new lower path. But GDP declining to a new lower path is a highly undesirable outcome and policymakers should be trying their hardest to make something else happen.
Less technically, while the wealth shock may impact people's proclivity for buying things it's not a shock to pour productive capacity. If meteor strikes destroyed 20 percent of our car factories, that would reduce potential GDP. If people just start buying fewer cars then we have a failure of demand management.