Before the compressor shut off, it makes a loud knocking sound

https://www.youtube.com/watch?v=sLR2vKxgwbM

A freezer compressor is what pumps chilled Freon -- or another cooling agent -- through coils that line the freezer compartment. ... The cooling agent inside the compressor is sensitive to being moved around, which can cause knocking noises. Also, loose components can cause knocking sounds.

I had accidentally overcharged a unit with freon one time (r410a freon), and when the unit stopped, the compressors rotor would spin backwards and make a loud "knocking" noise. This was on a scroll compressor, not a reciprocating compressor. Also, most compressors have a check valve, allowing freon to circulate in 1 direction only. And if it fails, when the compressor stops, the freon will rush opposite its normal direction of flow, and will sound off as a knocking noise(again, I've seen that on a scroll comp). That may make your indoor coil shake. I've seen/heard that make the copper lines shake but never the coil. Hope this helps! And FYI... Most ac service techs can check "superheat and subcool" as well as freon pressures. Without checking these 2 temperature measurements, we are just guessing as to how much freon is in the system. Make sure to ask politely beforehand for your service tech to do so PROPERLY when he checks the freon levels per factory specs, which should be on the units technical data located on the outdoor unit.

Pull the fridge away from the wall and inspect the compressor. Your description sounds like the compressor is hitting something. It is rubber mounted and usually can be pushed away from whatever it is hitting.You do not want to jamb something to stop the noise, as the compressor needs to move freely. Many compressors shake during start up and shutdown, and this is considered normal. Abnormal if the compressor hits something during this movement.

If this noise happens when the compressor turns on and shuts off it is called a compressor knock. All the internal workings of the compressor are supported by springs, over time the springs wear out and become weak. When the compressor stops or starts the tourq causes the internal parts to hit aginst the casing of the compressor. Sounds like a clunk clunk clunk noise. If you can deal with the noise do not go out and replace the compressor cause it will work just fine like that.

If the noise is loud enough that it sounds like somone knocking at your door then it is probably going to be the compressor. There are internal springs and is possible one broke. The only solution is to replace the compressor. It is also possible that the condencer fan motor is hitting something as well when it shuts off. You would have to look at it from the back as it shuts off after running.

check te rubber mounts at the bottom of the compressor
the rubber rots after some time and the compressor moves on shutting down as the knocking could be that noise

Well you may want to have a tech come out and check the freon level, but mostly when going into defrost, some units make alot of noise, the freon is reversed in the unit by way of the reversing valve, it makes a whooshing sound like freon is draining off, as far as the knocking noise, could be as I said in the beginning, might be low on freon, but it could be that, this particular unit does this, I have had units make some really strange noises in the past but functioned perfectly, hope this helped, please let us know, thanks again,
mr.grzz

There are springs inside the compressor that suspend the motor. When one or more of those springs break then the motor will knock against the casing when it shuts down and loses centrifuge motion. The compressor will continue to run up until the point the it beats itself to death, which could be next week of next year. There's no way to tell. The only solution is to replace the compressor.

the compressor has a loose or broken spring inside the compressor, unfortunatly it can not be repaired without replacing the compressor, it could last many more years and it could quit as we speak.

best thing is to let the neighbor know of the problem and what is the repair that way they won't think you are ponning off the machine to them, it may outlast your new one, time will tell

Does the sound occur when the compressor is starting or shutting down? and only lasts for a couple of seconds? I had one do the exact same thing. Sometimes it would also wake me up at night. If so, I'm afraid he is right. On the bright side, it worked fine for years. I gave it to a girlfriend when I purchased a bigger one and it is still working today. The only thing you can do is change the compressor, which is probably not $$ practical.