Final answer:
Fence trimming is the most flexible method used in CAD applications, where the user drags the cursor to create a 'fence' that trims intersecting entities.
Step-by-step explanation:
The trimming method that is considered to be the most flexible and requires the cursor to be dragged over the entities to be erased is known as fence trimming. This technique is commonly used in CAD (Computer-Aided Design) applications. When a user chooses the trim command, they can drag the cursor across the screen to create a 'fence' that intersects with the entities (such as lines, arcs, circles) that need to be trimmed. All entities crossing the fence will be trimmed or extended to meet the nearest intersecting object or boundary.