Many years ago while working as a technical service engineer for an a/c manufacturer I was called to a shop with nine 10hp splits.
The local sub station had a problem & one phase had failed.
The a/c units had continued to run for a period of time on 2 phase & all nine compressor motors had burnt out.
I had to attend a site meeting with the shop manager & a representative from the shops HQ, the mechanical services consultant,the mechanical services a/c maintenance contractor, the electrical maintenance contractor & engineers from the power supply company.
Alloction of blame for the cost of replacing the compressors was the agenda.
The power supply company advised that the contract did not garantee the correct power supply & therefore no claim could be made against them for the loss of one phase. They advised that it was the responsibilty of the end user to ensure that adiquate phase loss protection is installed to protect electrical equipment.

I had to advise that the manufacturer of split systems do not include phase loss protection as standard.

So the enduser had to cover the cost & consider if they would upgrade the complete chain of shops to include some phase loss protection.

If you look at manufacturers of splits & vrf you wont find any specific phase loss protection component in wiring diagrams or specification. But you will find that they will all stop & therefore save the compressor when the phase which powers up the circuit boards, safety circuits & transformers is lost.
But if the circuit boards, transformer & safety circuits are all powered from one phase then when any one of the other two phases fail for any reason the outdoor unit does not see this & the compressor continues with one or two phase & burns out.
So the unit will protect itself by default if the phase which goes down is also the phase which the unit needs for the controls.
You will find some a/c units use one phase for the transformer & another for the circuit board & another for the safety circuit. So if any phase fails then the unit will stop & save compressor damage.
But nobody seems to consider this as a design benifit ,,, until that is they have to deal with an expensive failure due to the loss of a power supply phase.