Die back
Definition 1 of 2
Pro Tip 1/3Seasonal Cycle
The phrase is often related to natural seasonal patterns in plants. 
Expect the perennial herbs to die back in autumn.
Pro Tip 2/3Not Permanent
In gardening, 'die back' doesn't always mean the plant is dead; it may regrow. 
Although the bushes die back, they will return each spring.
Pro Tip 3/3Observational Cues
Look for visual cues like browning leaves when plants die back. 
The hydrangea starts to die back when its leaves turn brown.