15-year-old fridge goes "clunk" at end of cycle
Sounds like a broken  or worn-out "vibration damping mount.the inertia of the internal moving parts at shutdown will cause the hole compressor to rotate up off  of the mounting  and slam back as gravity and the rubber nounts return it to its normal position. Common caus of the noise you describe. 
Fix find a similar mount to replace the broken one. At a used appliances store,or appliances disposal site for free,or order from the manufacturer.
  Gumby stay flexible.