Why is living muscle tissue seemingly able to restore its shape under force, while dead tissue is not?
Capillary refill time is defined as the time taken for the capillaries to refill after the blood in them has been squeezed out by pressure. It is widely used as a quick way to determine the effectiveness of the circulatory system in humans by doctors. 

In a normal living organism, the capillaries will take time to refill after they have been emptied. Muscle volume consists of the cell volume (which is fixed in the absence of lysis), the blood, as well as lymph and other intracellular fluids (which will be displaced elsewhere when it is deformed by pressure). 

When the organism is dead, there is no more circulation in both the blood and lymphatic systems, and therefore any fluids squeezed out by pressure will remain elsewhere, and the deformation is permanent without any regulatory effect by the circulatory system.