Additional question, if any, how much extra coin would a low income citizen get? What was the poverty line for citizens?

To sort of answer the first question, there is little we know for sure about the day to day life of lower class Romans. Written records were created by upper class and wealthy Romans. It’s fair to say that it was not overly pleasant to be a peasant, but the specifics beyond second hand reporting by politicians and aristocrats are unknown. If the person you’re talking about didn’t have a proper occupation and begged, they would not need many coins, since the Cura Annonae (grain dole) was free since before the empire was formed. If the person did have a job, they would probably be an unskilled day laborer, hired and paid on a day to day basis for various construction jobs or other manual labor. Any money made would be spent quickly on renting lodgings, also daily, and other necessities like clothing. Living hand to mouth leaves little room for accumulating savings.

To approach the second question, while banking did exist in Ancient Rome, it was mostly something only the wealthy engaged in. Temples served as banks, and priests managed and recorded deposits, loans, and withdrawals. There were, however, the mensarii, who were pubic bankers who served to prevent the poor from rising up due to economic stresses during exceptional circumstances of economic distress. If you owed enough debt, you could be put into slavery, and the mensarii operated a public bank designed by the state to reduce the level of debt and possible unrest.

In conclusion, if you had a coin to stash, I can give you no more information than what I would do in the circumstance. A bank would not be used, as the banks available for the poor were designed to reduce debt as opposed to hold deposits. You would probably want to spend the coin on something you need more than anything.