I work for a Housing Authority in NH, but if you are receiving subsidy from a HA, the rules should be the same. (Other places can get subsidy, that's why I ask.) Your portion of rent is likely based on 30% of your gross income, with a few minor deductions.
Income is separate from assets. If you are not talking about regular predictable income, then your rent should not change. You are allowed a certain amount in assets before the interest is counted as income, and that number is between 5K and maybe 50K depending on the HA. You may want to ask. (Or you can message me and I'll try to be more specific.)