How to safely dispose of a damaged lithium ion battery?
Be clear there are two levels of "damaged": bulging, and breached.

Li-Ion batteries will have  single thermal event: once the airtight case is breached they'll rapidly discharge: if there's enough energy in the battery they'll heat up perhaps to the point of catching fire.  Once that's happened there's no more energy, it's just toxic waste.  In my experience the batteries just get hot and smolder.

Thus you have one more option: (1) discharge the battery as much as you can, (2) move into a completely safe space, puncture the battery, let it heat up (or not), and then dispose of it like any other hazardous waste at a Household Hazardous Waste facility.  At that point it's not a battery, it's chemicals.

https://www.epa.gov/hw/household-hazardous-waste-hhw



Practically what I do is tape over the terminals of the old battery, and gently deposit in a battery collection facility.  They're the experts: it's up to them to determine where each battery goes.  Every collection center already has to deal with the potential for fires, and the need for safe transport.



Frankly the advice to use a special $100 bag to dispose of such batteries is bad advice.  Almost nobody will ever do it: the battery will either remain on the shelf or get chucked in the general trash, an outcome worse than the problem you set out to solve.