Well some of them, along with Ruth, must have survived because Ezra saw them in the Land of Israel as late as the 4th century BC:
"Now when these things were done, the princes came to me, saying, The people of Israel, and the priests, and the Levites, have not separated themselves from the people of the lands, doing according to their abominations, even of the Canaanites, the Hittites, the Perizzites, the Jebusites, the Ammonites, the Moabites, the Egyptians, and the Amorites".[Ezra 9:1]
You know....I think part of the problem here is that I pinged you too late in the thread.
[Numbers 21:26] For Heshbon was the city of Sihon the king of the Amorites, who had fought against the former king of Moab, and taken all his land out of his hand, even unto Arnon. The King of the Amorites had taken all of Moab away from them......to the River Arnon. This was about half of the Kingdom of Moab. The land above the river was now occupied by the Amnorites and the surviving Moabites lived below the river and south to Edom. This is directly east of the Dead Sea. Above the River Arnon and north to the River Jabbock was the captured territory of "The Plains of Moab". Here is where Moses settled the people prior to crossing the Jordan to fight the Canaanites. [Numbers 21:21-25] And Israel sent messengers unto Sihon king of the Amorites, saying, Let me pass through thy land: we will not turn into the fields, or into the vineyards; we will not drink of the waters of the well: but we will go along by the king's high way, until we be past thy borders. And Sihon would not suffer Israel to pass through his border: but Sihon gathered all his people together, and went out against Israel into the wilderness: and he came to Jahaz, and fought against Israel. And Israel smote him with the edge of the sword, and possessed his land from Arnon unto Jabbok, even unto the children of Ammon: for the border of the children of Ammon was strong. And Israel took all these cities: and Israel dwelt in all the cities of the Amorites, in Heshbon, and in all the villages thereof.
[Numbers 21:31] Thus Israel dwelt in the land of the Amorites. This area is called in scripture as "The Plains of Moab". North of the River Arnon, east of the Dead Sea and the Jordan River all the way north to Gilead. These lands previously belonged to the Moabites and they (the ones that lived there) were defeated by the Amorites. They (Amorites) now possessed "The Plains of Moab". Along comes Moses, Joshua and the Israelites and they take "The Plains of Moab" from the Amorites....killing them all: [Deuteronomy 2:32-34] Then Sihon came out against us, he and all his people, to fight at Jahaz. And the LORD our God delivered him before us; and we smote him, and his sons, and all his people. And we took all his cities at that time, and utterly destroyed the men, and the women, and the little ones, of every city, we left none to remain.
The Israelites now possessed "The Plains of Moab". All previous residents had been killed. The Moabites who lived in that part of Moab had been killed earlier by the Amorites and Moses had now seen to it that the Amorites were destroyed. These 'Plains of Moab" are the areas that were promised to the tribes of Gad, Rueben and Manasseh if they crossed the Jordan and helped their fellow Israelites defeat the Canaanites. They did and then returned to these "Plains of Moab" which they then called home for about 700 years. This was where Ruth had been born and lived about 100/150 years later. She was an Israelite.....of Moab. This is the same as my wife being described as a German/Californian. California used to be the possession of Spain and Mexico but is now held by the U.S. We still call it California and my wife is accurately described as a California woman.
Baja California is still around but their northern territory has been held by us now for over 150 years. We still call it California.....and folks still live in Baja also.
You are correct. The Kingdom of Moab was still around years later....much smaller and a shrunken population....but still around.