The flame propagating into the lean region of the stratified mixture below the lower flammability limit was supported by the burned gas behind it. In this study, the effects of the flame stretch on this supported flame was investigated numerically. The supported flame and the burned gas behind it were linked to the counterflow flame configuration of the lean mixture and the hot nitrogen. The results show that the flame stretch deteriorates the reaction of the supported flame. The production of CO and unburned hydrocarbons increases with increasing the flame stretch rate. Moreover, the self-sustaining flame in the flammable range turns into the supported flame by the intense stretch.