What is the significance of the missing L structure on the farm?

The structure missing from the house (the L) connects the main part of the house with the woodshed and the cow-barn. The "L" itself is a symbol of life, it connects the farmer with the soil and signifies warmth, nourishment and hope. The absence of the "L" symbolizes the home's emptiness and lack of life, it also signifies Ethan's hopelessness.