I think there is nothing to worry about this recent development on Bithumb since it could only lead to a corporate takeover and will not stop its daily operations.
There is a real reason to worry. Many companies in recorded history have fallen due to quarrels, legal battles, and the like which involve high company officials against fellow officials. It cannot be said that the operation is business as usual. There might be a ripple effect and no one can tell how the entire company will be affected.
Transfer of shares of stocks to another owner or corporate hostile takeovers are a regular thing in everyday corporate environment and it doesn't mean the company is already doomed.
With Bithumb's status as one of the large crypto exchange in Korea, traders will have second thoughts on leaving it altogether, not unless they find a better alternative exchange which I doubt could be hard to find at the moment. Imho.
South Korea has a lot of crypto exchanges which are as reputable as Bithumb. The country has Huobi, Coinone, etc.
Aside from Coinone, Houbi is originally a Chinese company based on Singapore. Huobi Korea is only a subsidiary of Huobi unlike Bithumb which is originally from South Korea.