Below I'll give you a partial answer by talking about research on poverty traps. Before that, though, let me point out that it is a bit difficult to find any theory that is not motivated by observations. Theories of poverty often have a trap because theorists want to explain why there are locations in the world where everyone is poor, and other places where everyone is rich. Multiple equilibria is one popular way to explain this simple fact. My development prof in grad school would always hide a slide with Admiral Ackbar somewhere in the discussion of a new development model: "It's a trap!"
Maybe the first model of a poverty trap was the big push model of Paul Rosenstein-Rodan in 1943. Rosenstein-Rodan built on insights from the work of Allyn Young who died in 1929. Due to externalities, the investment by individual firms is not enough to lift a country out of poverty. The government needs to come in and subsidize large investment projects.
The more recent poverty trap literature is legion. I doubt it is their original idea, but Banerjee and Duflo talk about the nutritional poverty trap in their recent book, "Poor Economics". If you are too weak to work, you can't get money to buy healthy food. You need healthy food to make you strong enough to work.
If there is learning by doing, economic specialization can be harmful. Alwyn Young (1991) is about how opening up to trade can lead poor countries to specialize in traditional industries which have no room for productivity improvements.
Rather than go any farther into the taxonomy of poverty traps, I will just direct you to a fairly recent survey by Stachurski and Azariades (2005) which discusses many other mechanisms which lead to a poverty trap.