No. Additional living expenses are expenses you incur on a regular basis that are temporarily increased as a result of the loss. Closing costs are not a "living" expense.
Living expenses are: food, utilities, rent. Example: you have to pay rent on an apartment while your home is repaired. At the same time you are paying your mortgage.
I think you mean ADDITIONAL living expense. And the answer to that is no. Not only that, if you don't actually rebuild on the same footprint as the old house, you don't get the replacement value - you only get the depreciated value.
You'd get the additional living expense while you were rebuilding. Once you decide not to rebuild, the additional living expenses cease.
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