I would say yes, it is relatively safe to start your own business in Taiwan. You can own 100% of your business/company, and Taiwan’s business environment is rather stable and safe. However, the banking system in Taiwan often asks for gaurantors when doing transactions or applying for loans.
So it is imperative to make sure that your Taiwanese partner (if there is one) cannot withdraw money or change any financial status without your seal or signature.
Overall, starting a business is safe in Taiwan, but an entrepreneurs has to know how to protect his or her own business.