My experience is with a complex turboprop system was on the Emb 120, with the Hamilton Standard 14RF-9 turned by a PW118. I beleve the Ham was an option on the SF34. Early overspeeds with this prop system were attributed to a failure of the pitch change mechanism - the nut that actuated the transfer tube would wear in the thread area, until control was lost of pitch. At that point no amount of governors would alleviate the condition, as they all merely modulated oil pressure on the very mechanism that had failed. In flight, the fuel-topping governor was also irrelavant, as the centrfigual twisting moment was quite sufficient to drive the prop towards fine pitch. One fatal E120 accident was blamed on this failure mode. The metallurgy in the mechanism has been changed, and the problem appears contained at this point.
When looking at the PCU schematic, it also becomes clear that a failure in an oil line in many conceivable locations will result in a prompt overspeed. The troublesome thing about an overspeed is that once it happens, the failure mode is usually of the sort that it can't be fixed with pilot input, be it a feathering solenoid, an electric feather pump, or what have you.
As far as the question "how serious?" When practicing in the sim I've never survived and uncontrollabe overspeed. When the propellor goes to flat pitch at speed the blade angle of attack is negative to the relative wind - it's comparable to selecting reverse. Major drag is created, compounded by massively disrupted airflow over the a large portion of the wing, and horizontal stab. The aircraft is nearly impossible to control in pitch and yaw.
A King Air driver demonstrated the problems nicely when he selected ground fine in flight to expedite a descent. All was well until he advanced the power levers, one engine came out well before the other, control was lost, and the aircraft was lost.