I played a version of this on Zoom as part of a Columbia University program [1] designed to simulate the conditions of re-entry from prison, which have considerable structural similarities to poverty and homelessness. The Zoom game is based on one played in person with "stations" representing different institutions and "tokens" representing stuff like money, birth certificates, ID cards, etc. Your hypothetical scenario is quite a lot like the mechanics of this game. I'm working on building a single-player software version of it because the live simulation is rather difficult to stage!

[1] https://www8.gsb.columbia.edu/socialenterprise/initiatives/r...