When you activate topological symmetry on a mesh that is not topologically symmetrical, partial topological symmetry activates by default. You can use partial topological symmetry to edit parts of a mesh that are symmetrical, even if the mesh is not symmetrical overall.
To edit a mesh with partial topological symmetry
The local area around the selected edge must be symmetrical.
For example, the model below is not topologically symmetrical, because it doesn't have an equal number of faces on each half. However, there are parts of it that are topologically symmetrical, and you can use partial topological symmetry to edit them. For example, the local area (yellow) around the selected edge (red) is topologically symmetrical, so you can make symmetrical edits in that area.