Probability and possibility isn't the same. The possibility of a very rich person becoming poor is real, of course it's real, you can get poorer, but probability is lower. How many people in the world had a 1+ billion dollars networth, and became poor? Like ended up with under 1 million dollars networth by their death? I can tell you that not a lot, so that means if you are rich enough, you will never be "poor", you could be less rich, but never poor.
Before anyone can get rich, he would have planned his life to that point apart from people that win the lottery or got some quick money through scamming or other illegal ways. The ones that merit the wealth had a plan that they followed and the plan will involve having different investments that they got through diversification. With diversification, they can't go broke that quickly, they might lose some amount of money but they'll be able to recover with the other business or investment that they own. The possibility of a poor man getting rich should be higher than the possibility of a rich man going broke. The rich have well planned life and will not take risk that can make them lose all their wealth. Any rich man that lost everything out of no where would be lying and only filing for bankruptcy as cover up, in trying to avoid the federal government investigation into their wealth.
If we're just talking about probability then for sure there is a tendency for a rich man to become poor especially if he will be using his wealth to things that won't generate money or to extend it. No amount of money is enough if your lifestyle is just continuously increasing because eventually everything will be consumed or outnumbered by your expenses. Point of view is respected but I think rich people are least likely to be poor atleast in most instances. As you've mentioned their lives are already planned and supported by generational wealth and that means it won't revolve solely with business but also assets that increases its value in the long run which will help them sustain their wealth or slow down their transition to poverty.
On the other hand, not all hard working poor individuals are succeeding in real life. Check on most of the farmers (except for farm owners); we can't deny that they're really working hard to make a living. Even if their children finishes studying, that won't guarantee wealth. Wealth doesn't only mean you can buy the things that you want. You could live a better life through hardwork and perseverance but wealth is on another level (yes we do have our own definition of wealth but atleast in this context).