Removing the boundary doesn't really make sense -- if you allow people to go into negative dollars but still be able to give a dollar each tick, then there's no longer a finite amount of money in the system.
Sure there is, it's just effectively a zero interest debt instrument. Imagine that everyone is exchanging IOUs, instead of physical dollars.
You misunderstand. The parent meant that the amount is infinite, so the property that eventually every state will happen is no longer there.
Wow, a mathematical explanation of how uncapped debt reduces wealth mobility.
You're kidding, right? No way a generic observation about a markov chain (which doesn't even model interest) implies that "uncapped debt reduces wealth mobility".
So, with typical debt, interest rates are higher for debt than for savings. Does seem that a) removing the cap, and b) introducing interest on savings < debt would trap some people in poverty?