Either brace it, stake it, cut it, or give it away. Just kidding about the 4th option.

I often use a huge rock in some of my pots to brace a begonia if it is "flopping over". A big rock also helps discourage digging squirrels (all kinds of tips here). It can also be used to weight a recently cut plant in the pot you want it to root in. Works quite well.

A stake works too but then you also need to tie the plant to the stake. Plus you have to usually cut the stake to size and why waste a good stake for a floppy begonia? You could try 2 bamboo skewers in an X shape to support it too. Bamboo skewers are cheap, disposable, and can be used as dibbles for starting cut leaves. The only downfall is they can mold in a very moist environment - I don't recommend these for terrariums due to that fact.

Cutting works as well - maybe not what you want to hear but at least you can start a new plant with the cut top. See how easy that is?

Just to make sure, do you mean the rhizome is leaning, or the petiole of a single leaf? Don't think I've ever seen a Rex for sale that was big enough to lean from the rhizome, but that's not sayin' much, just a thought... and maybe someone gave it to you, IDK.