Can you line an urban planter box with a plastic bag to keep the soil in? Yes, technically, but I would not recommend using an ordinary plastic bag as a closed liner. A plastic bag can stop soil from washing out through gaps, but it also tends to block drainage and air exchange. In an urban planter, where drainage holes may be few and airflow is already limited, that can create a perched water table: water collects above the plastic, the soil stays soggy, and roots are deprived of oxygen. That is exactly the condition that encourages root rot.
The safer approach is to line the box with landscape fabric, geotextile fabric, burlap, or a permeable coco liner. These materials hold soil in while letting excess water pass through. If the planter has drainage holes, cover them with fabric so soil does not clog them, but do not seal the bottom. Use a free-draining potting mix, and make sure the box is slightly raised so water can escape.
If you must use plastic, do not use a sealed bag. Use perforated plastic or punch many holes in the bottom and lower sides, then cover the perforated plastic with landscape fabric so soil does not block the holes. Keep the drainage path open, avoid a loose plastic pouch that traps water, and check moisture regularly. Even then, plastic is not ideal long term because it can become brittle and restrict airflow. In most urban planter boxes, landscape fabric is the better choice: it keeps soil in, supports drainage, and lowers the risk of root rot.