What you’re referring to in the “killed” vs “dying” is a diyuk that messianic lubavitchers make in a rambam, which chooses to use rhe word killed rather than death. This would beg the question…why would it make a difference? If the point is that a candidate for moshiach must accomplish his mission, then once he leaves the world, he has not fulfilled that task and is therefore disqualified for being considered moshiach.
Then the question remains why the rambam chose the word “killed” , and there’s a very simple reason – he was coming “la’afukei” to exclude, the christian claims that yushke was moshiach. There is only one opinion in the gemara that moshiach can be “min hameisim”, from the dead, and that if he is so he must be as great as Daniel, which the lubavitcher rebbe most definitely was not.
Yes, yaakov lo meis. Eliyohu also didn’t. But everyone else… Moshe rabbeinu, dovid hamelech….the lubavitcher rebbe was greater than all of them? it just seems that they’re trying to find a source for the idea of someone not dying, and then attributing it to their rebbe, because it’s impossible that their leader would leave them – also, the divinity complex makes his death impossible as well.