As a rule under potential is not antenna cable, but ungrounded PC case, which is due to common design of power supply units is under potential of 55 or 110 vols relatively to grounded shield of TV cable of common antenna. Antenna connector of TV-tuner, as any other connector on PC case, has galvanic connection to PC case and by connecting antenna cable you are "grounding" the PC and all devices that connected to it. When the power supply unit works properly, the maximal leakage current through such "grounding" does not exceed 1mA, which can't harm you and the tuner, except of unpleasant feelings. One of the possible consequencies of such grounding may be the noise and shuttering of the picture on PC display. In this case you need to put antenna ground loop isolator in break between antenna cable and tuner, which provide full galvanic isolation on direct current and greately decrease leakage on alternative current.
More serious problem may arise, if TV antenna and PC case are grounded, but grounding is performed in different places and there is voltage pickup between grounding points. In this case the leakage current through antenna connector will depend from a large set of factors, such as method of grounding, distance between grounding points, air humidity, number of power consumers and TV sets in building, time of day and many others. Large leakage current may result in heating and destruction of antenna cable and connector, noise pickups on PC display and connected to the same antenna TV set, triggering of protection devices known as Residual-Current Circuit Breaker (RCCB), Ground Fault Circuit Interrupter (GFCI) or Appliance Leakage Current Interrupter (ALCI). As in the first case you may solve this problem also by using antenna ground loop isolator.
And the most serious situation – malfunction of PC power supply unit or other devices connected to antenna cable, or improper connection of grounding contact in electric outlet. As a result, the PC case may turn to be under direct power potential 230/110 volts. On connection of TV cable to PC case there will be a short circuit in electrical power network burning and fusion of cable, connector and PC and triggering of automatic power breakers. Although the using of antenna ground loop isolator may hide this problem it is strictly urgent to solve the problem with the help of qualified electrician.