When income falls, demand for inferior goods increases (shifts out). This may seem odd at first, but it makes perfect sense once we recall the characteristics of an inferior good. For a good to be an inferior good, there must be an alternative, more preferred, product whose price is higher. When income falls, the more expensive alternative becomes less affordable, so more of the inferior good is purchased instead.
Suppose the graph to the right represents some consumer's demand for ramen noodles. When she enjoys a somewhat higher income, our consumer's demand for ramen noodles is given by demand curve DI1. A reduction in income causes our consumer to have to purchase more ramen noodles because she can afford less of the foods she prefers. This shifts her demand for ramen noodle out to DI2. When her income is higher she would only buy 6 packets if they sell for 50 cents and only 3 if they sell for $1.50, but at a lower income she will buy 13 at a price of 50 cents and 10 at a price of $1.50 per pack.