In most cities, the honest answer is: sometimes, but not always. A standard urban trash can usually does not need a heavy engineered foundation, but it often does need a stable, level base and proper anchoring. If the can is going on a sidewalk, plaza, or other public hard surface, crews commonly set it on a concrete pad or a reinforced mounting plate and bolt it down. That keeps it from tipping in wind, sliding when people lean on it, and being moved or stolen.
The exact requirements depend on several things: the type and weight of the can, how much foot traffic the area gets, the soil or pavement condition, drainage, local weather, and city codes. A lightweight temporary bin may only need a flat surface, while a large public litter bin in a windy or high-traffic location may need anchor bolts, a concrete pad, or a specified mounting system. Good drainage matters too, because water pooling around the base can damage pavement and make the area messy.
So, do urban trash cans need special foundations? Usually not a complex structural foundation, but often a simple, secure base and anchoring system designed for the location. Check local regulations and manufacturer instructions before installation, especially for permanent public bins. That is the safest and most practical approach.