Do the refrigerators and air conditioners that use CFC or HCFC cause damage to the environment even when they are working normally. I mean, is there any gas emission under normal conditions when the AC or refrigerators are well maintained and there is not any leakage. ( I am asking this question in relation to the working of AC and refrigeration systems, hoping to not make this question off topic here)
To touch on a deeper aspect of the question, let's mentally uncouple the working cycle of an appliance from the global use cycle of the refrigerant, from its manufacture to its decomposition.
Considering the latter, a refrigerator always ends up in the waste, often after suddenly losing its working gas anyway. A residential HVAC system using the old R-22 refrigerant (which is no longer manufactured, unless illegally, which actually happens) will eventually be replaced with one using a different modern working fluid with a shorter atmospheric half-life and/or lower ozone depletion potential. The R-22 has now become quite expensive in the US, and is carefully collected by technicians replacing these old systems, to be reused to replenish leaking outdated systems still in use (or, hopefully, disposed of chemically: likely in the EU, where the recharging of R-22 systems is already illegal, AFAIK; less so in the US and Canada, where it is allowed to be reused; unlikely in China, speaking of largest users). Where it's all going to end eventually? No collection is perfect; the system do leak; and the natural decomposition time constant of this stuff is on the order of a thousand years. Significant part of the R-22 currently in use will probably end up in the atmosphere in a few ten years anyway.
So while the “normal” working cycle of any single refrigeration or HVAC system is a closed loop without loss of the working fluid, the “normal” lifecycle of the total produced fluid is widely open.
No, the refrigerant is in a closed loop. CFCs were used because they are not noxious to humans. Other systems use NH3, which is dangerous for humans when there are leaks. https://www.thestar.com/vancouver/2018/08/30/20-mistakes-that-lead-to-fernies-deadly-ice-rink-ammonia-leak.html
Household refrigerators are completely sealed and do not leak unless they are cut open. This is because the electric motor that drives the refrigerant pump is actually built into the piping network- so if the pump leaks, the refrigerant does not escape the system.
Refrigeration systems used in cars for AC are susceptible to leakage because they are driven by the car's engine via a belt and pulley, which requires leakproof rotary seals on the pump, and the various components of the system are connected together with clamped hoses that have refrigerant inside. Although they are not supposed to leak, they commonly do, and they can release refrigerant into the environment through a leak even when they are not operating.
The refrigerants in current use have been specifically designed to be much less harmful to the environment than older CFC compounds, and it has been illegal for years to discharge CFC's into the air when repairing car AC systems.
As stated by Niels Nielsen, household refrigerators do not leak under normal conditions. However, air conditioners in your house and your car have seals that leak very little or none when they are new, but over time, they do indeed leak refrigerant. This means that refrigerant for air conditioners will eventually leak to the environment.
Regarding any illegality of discharging refrigerants to the atmosphere, there are times when a bit of air gets into an air conditioning system when it is recharged. This air collects at the condenser, represents a non-condensible component in the refrigerant stream which decreases the efficiency of the system, and must be removed by blowing it out of the system, usually to atmosphere. I haven't personally watched every move of the technicians who have performed maintenance on my A/C systems, but I have seen a few times when these technicians did not capture the small amount of refrigerant that they had to remove from the system to eliminate non-condensibles.
Regarding harm to the environment, MANY substances can be used as a refrigerant. The substances that are chosen have to meet quite a few constraints, including price, toxicity to humans, harm to the environment, boiling point in the proper range, a high enough molar mass to limit the size of the equipment that uses them, installed equipment cost that can use the given refrigerant, etc. Very often, it is difficult or impossible to meet all of the constraints. The best example of this is the fact that the most environmentally friendly refrigerant may be anhydrous ammonia, which is still used in a few applications. Obviously, the general public would NOT want to use this substance as a refrigerant in their home or auto, as any small leak of anhydrous ammonia is extremely noxious and toxic.