Actually, the manufacturers take great pains to ensure that emulators do stay in synchronization with the target system.
Which you, while still babbeling about “synchronization” which I STILL do not know what has to do with it, in a previous post stated as a deficiency of an ICE.

Erik states: "That is not "synchronization", that is emulating." Richard: ... Emulating is what IT does. Running the code in its ROM is what the target system does.
For a current uC (e.g. P89V51Rx2) the emulator runs the code and so does the chip. Both with no external connections to get the program. If there was ANY difference between what happened running with an emulator (obviously only till a breakpoint was reached) it woyuld not be an emulator, it would be something else.

They can and do, but I don't know how well, how costly, and what "additions" e.g. pods, etc, I'd have to buy before I could get useful work out of their product.
So you ask half the question, get a yes, and then keep refusing the possiblity

Erik states: "...No simulator will ever be "true"."
and I say, This is exactly why I prefer the resident debug monitor.
I make a statement denying what you said about a simulator (it can have exact matching) and you reply with “I prefer the resident debug monitor”.

Erik

PS
as said earlier, it does not matter what you want (which you keep talking about) you can only have what is available (which I talk about).

You may have seen wonderful things for the PC, the ACME, the PHnox, the Unicorn or whatever processor - here we discuss the '51.