Greetings!
It is not surprising that you are confused or even that the Witness lady is also confused as the various teachings have morphed throughout the years (and I am not even referring to the Russell Era) on this topic.
In short the current belief/teaching is that there will be some of the 144,000 aka anointed left on Earth at least during the start of the Great Tribulation. (The Great Tribulation is a period of time broader than the "Day of Armageddon". Armageddon is viewed as the culmination, the final war of the Great Tribulation). It is generally thought that some of the 144,000 will be left at the conclusion of the GT/Armageddon but expressions about this are more circumspect and vague. It is also vague as to how long into the New System/Millenial Reign (which begins immediately after Armageddon concludes) such anointed might live and help direct the earthly aspects of God's Kingdom, but it is thought that since these person's place is ruling in heaven (as kings and priests) that those living will not see death but be changed in "a twinkling of an eye" into their spiritual/non-material existence.
The basic scriptural reasons for the above come from two lines of reasoning:
1. The Scripture that says that the days of the tribulation will be "cut short for the sake of the holy ones" (to preserve them alive)
and
2. The FDS doctrine teaching in general. Because this doctrine holds that this slave continues to provide food blah, blah, blah until being given charge over everything. The view being that the master's man will be in charge over the domestics and around until the new system.
-Eduardo