I've been watching the SM anime, and they've talked several times about needing to catch Bewear, but so far they haven't actually done it.
Bewear is a recurring Pokémon character in the anime who appeared in Pokémon the Series: Sun & Moon. She seemingly appointed herself as Team Rocket's caretaker during their stay in the Alola region.
It has never been captured, but it takes care of them.
Source: Experience (I've watched the anime) and https://bulbapedia.bulbagarden.net/wiki/Bewear_(anime)
No they do not end up catching the bewear they end up leaving there Pokémon so they can be protected from there boss
