Well, it's not without controversy, surely. You're (a) focusing on the very short term; presumably people would only commit one burglary under this model over their entire lifetime; and (b) you're not being generous to the original case but taking it at a very literalistic level. It would be more generous to the point to suggest that the $40k/year would be spread out to support low-income folks who might have otherwise needed it. So, about 1% of American adults are imprisoned (and about 2% are on some form of probation or parole). On the other hand, 16% of our population lives in poverty. So we might reasonably expect to instead reduce the prison population by, say, half, and kick back that money to the impoverished. The salient point is that this would give a (1/2) * 1% / 16% = 1/32 dilution of the money, so we're talking about giving all the poor people in the US $1k - $2k per year in order to reduce the rate of crime being committed. This makes their finances at least 5% better (the poverty line is about $20,000 for the 16% statstic).

So the more-generous question is, would being at least 5% better off financially reduce crime more than the 50%-shorter sentences for crime would increase it? I have no idea.