"Poverty" may nicely compress many details, but isn't particularly useful in this instance, as we are discussing the specific point of technical ability (as opposed to psychological feasibility, desirability of implementing such a plan, etc.) of a hypothetical rational low-income person to accumulate money in some form. It's not that impossible a requirement to make considerations depending on it irrelevant. Creative solutions exist: you can probably hide cash under a tree stump of something.

Noteworthy:

Being poor is knowing you really shouldn’t spend that buck on a Lotto ticket.