That's a great and very practical question! Dealing with a broken public trash can is a common urban dilemma. Here’s the most effective and responsible way to handle it.
First and foremost, do not try to dispose of a broken public trash can yourself. These bins are municipal property. The best and only action you should take is to report it to your city's public works or sanitation department. You can usually do this via a city website, a dedicated app (like 311 services in many cities), or a phone call. Provide the exact location and a brief description of the damage (e.g., "lid broken off," "hole in the side," "completely overturned"). The city will send a crew to assess, repair, or replace it.
Regarding recyclability: It depends entirely on the material. Most modern urban bins are made from durable, potentially recyclable plastics like HDPE or metals like galvanized steel. However, they are not meant for curbside recycling. Their size, weight, and often contaminated state disqualify them. The recycling, if possible, is handled by the municipality at a specialized facility when the bin is permanently decommissioned.
If, for some reason, you are directly responsible for a broken *private* bin (like from your home), check its resin code. Heavy-duty plastic bins (#2 HDPE or #5 PP) might be accepted by some bulk recycling programs. Metal bins are typically scrap metal. Always call your local waste hauler for guidance first.
In summary: For a public bin, report it, don't remove it. Your quick report keeps your neighborhood clean and safe. For private bins, contact your waste service provider for specific disposal instructions.