Welcome!
I offer you a different point of view - allow them to do a partial cash out, aka let them go south.
You see, 'ratholing' wasn't a rule to not screw over other players at table. It came about as control for the casino. It is now so ingrained into culture everyone says NO, but they don't actually know why, or the impact on the game.
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Here is
another discussion on the topic.
While I will argue that there is a place for this in poker culture, I wouldn't actually allow it at my game unless the majority was okay with it. I would also likely put in some sort of minimum limit, if you have more than 200 bb or Max buy-in, you can take off 50% of the difference in stack and the min 200 bb. So if its a 1/1 and you have 400 you can pull off 100.
There are other ways to achieve a similar result. Playing PLH (Pot Limit Holdem) would prevent the dumb mechanics of playing NLH in smaller stakes where there are less skilled players or the idgiaf players. It allows for less bluffing and focuses on better calls/raises/folds. What I find most dumb is the starting hand EV diff in holdem, its why its so boring to play, I said play but really its a wait for top starting hands and try to trap game, or try to bad bead someone with 2 random cards from a limp and hit the nuts on the flop. Other games are about making decisions based on dynamics of the game, this is more rewarding and enjoyable at least to me. (My argument here is to pick a better / more fun game, and you won't have people worried about going south at least as much)
Another way is to limit the buy in and not have a match or 1/2 stack option. Explain to your players they should at least have 3 buy-ins and with a cap, it effectively functions the same as going south in the long run.
If a player is limited to a max buy-in, then they can't get stacked for all of the winnings by someone constantly re-buy shove. Which is how it accomplished the same function. If you have players over allocating a bank roll you might also reiterate that the game is focused on entertainment and is by design soft to help newer players.
to be more direct and answer the OP - Partial cash outs are called 'going south or ratholing' its considered extremely rude because 99% of the population that plays poker is ignorant to the reason the rule was in place and now the dogma prevents anyone from being flexable in this way. However, there are other things we can do that will help players be winning players. For starters, we don't take a rake - you're welcome'