I think BNB will be fine. but I don't know about BUSD. but I'm also pretty sure Paxos will handle it pretty well. because even after this FUD we can see BUSD not dropping too far. and this is different from last year's UST or Luna case. However, we must still be prepared for the worst. so for a while I also converted my BUSD to USDT. Being careful is much better than being sorry in the end.

Recently we have seen a huge Dump in BNB price, as well as BUSD, is treated below $0.998. The BUSD price $0.998 seems not too low for many new traders but for the Whales and big investors its like, if they have $998000 USDT then they can get $1M BUSD, and later on they can sell it with an equal amount, so they do the trading but BUSD price dumped to $0.9959 which is a lot for the big investors.
The same happened for the BNB holders, as the BNB was traded at around $320 but recently down to $283 which is also a lot for the big whales.

All the Dump occur because of the SEC because they launch enforcement action against Paxos, the issuer of BUSD. Paxos says that it will vigorously defend itself, and the issue is going to court. But as per the CZ's recent tweet, "Ignore FUD, fake news, attacks, etc." it is clear that both BNB and BUSD will recover the price soon.

All the small investors and Newbies are advised to take extra care because if something bad happens then they won't be able to get their investment back and it will be the same case as LUNA and FTX as they were also considered Stablecoins like BUSD.