Clone your object
While there are a number of ways to (at least partly) do so, none of them are completely without flaws. However, don’t let this stop you from setting up one of your own. Select your (half) object and from the Edit > Duplicate/Instantiate menu chose Clone Single. Any changes made to your original object will automatically propagate to the clone but changes made to the clone object will not affect the original.
Symmetrize the polygons
From the Modify > Poly.Mesh menu choose Symmetrize Polygons. This will mirror all the polygons, creating the missing half of the model. Press [Ctrl]+ to switch to the Palette toolbar and click the W button in the Display Types section. In the viewport or an explorer, pick your original object and then right click to end the picking session. This will set the objects display type to wireframe
In the Viewports menu bar > Display Types menu, uncheck the Override Object Properties. Select the clone. In the Select panel, click the Selection button and click on the Visibility node in the pop-up explorer. In the Visibility PPG uncheck the Selectability checkbox. This will keep you from unintentionally selecting it. Finally, open the Visibility PPG for the original object and uncheck the Render Visibility to prevent it from being rendered.