“Are fixed dentures safe?”

Implant supported dentures are safe when the implants are placed by an implant  specialist and constructed so they can be periodically removed and cleaned. Optimum maintenance is required to minimize inflammation and infection. Well made fixed dentures are an excellent prosthesis for edentulous patients. 

Am assuming you are referring to a fixed denture retained by implants. Yes, they are safe but do require some regular homecare to maintain them.