The aim of this paper is to simulate the European natural gas system in extreme situations and to determine its weaknesses in terms of demand coverage. An assessment has also been made of the targets set for existing energy efficiency regulations and their effects on the coverage of future natural gas demand. This document assesses the potential for energy efficiency improvements associated with European countries and the effect of such improvements on the lessening of the natural gas demand. Once the efficiency improvement potential has been identified, the results of demand coverage in various scenarios of natural gas supply cut-off via pipelines were studied. The expected result reflects the study of the effect of the presumed demand reduction, due to the improvement of energy efficiency, on the self-sufficiency of the natural gas network and the improvement of energy coverage for EU countries. To carry out this study, an evaluation of the current infrastructures was developed, the existing resources were optimized, and the independence of the system was quantified in relation to the current situation of natural gas consumption at the European level. The proposed model has resulted in improvements in the coverage of the demand of certain countries and has detected those with systems that are not robust enough to face extreme crisis situations. The main conclusions are that the natural gas system has improved considerably from 2009 to the present, and that, in the event of massive gas cuts, there is a real risk of being unable to cover the natural gas demand of several countries with a very high dependence on gas from Russia.