Even if the price of the coin falls and the demand falls, as long as there is no fall in the hash rate, it means that the coins are not dying.
Yes and no. Miners might attempt to pump the coin they mine but it is not going to work out long-term (e.g. Bitcoin Cash - miners [Bitmain] were mining it even though Bitcoin was more profitable). Any coin is useless if there is no large user base and merchants who would accept it. The price is not the most important factor here, it is the demand.