Short answer: yes—replacement parts are usually available for an urban bench if a slat breaks, so you typically don't need to replace the whole unit. I've dealt with this exact situation, and the key is figuring out whether your bench came from a commercial site-furnishings brand or a generic/standard design.
If there's a manufacturer label or plate—often on the underside of the seat, on an end frame, or stamped into a leg—start there. Brands that supply park, campus, streetscape, and plaza seating typically sell individual replacement slats, either pre-drilled or as blank stock, plus the anti-theft or tamper-resistant hardware kits you need. You'll want the model name or number, overall seat length, slat width, thickness, and center-to-center bolt-hole spacing. Even if the exact color has faded, a replacement in a close finish will usually blend in after a few weather cycles.
If the bench has no badge, don't panic. Measure the broken slat or its neighbor carefully: length, width, thickness, number of holes, hole diameter, and distance from each end to the first bolt. Urban benches often use standard dimensional lumber—like 2x4 or 2x3 clearances in wood, recycled plastic lumber, or extruded aluminum slats. A local lumberyard, metal supplier, or online outdoor-furniture parts shop can often cut and drill a matching replacement. Many shops only need a clear photo and those dimensions.
One thing worth checking before ordering is the frame. If the broken slat pulled out because the metal frame is cracked, badly rusted, or stripped at the mounting point, replacing only the slat may be a short-term fix. Threaded inserts can sometimes be repaired or re-tapped, but if the frame is compromised, that's when you start weighing a full replacement.
So unless the frame is structurally damaged, a slat break is almost always a repair job, not a new-unit job. It's cheaper, faster, and much less wasteful.