Answer: Believe it or not, under the right conditions both tomato and pepper plants can live and produce for several years. So, your surviving pepper plant should be able to produce peppers this coming season. The problem with some plants is that when they ripen fruit, it saps the plant of energy and signals the plant that it has done its job (producing seeds) and it can die off. I'd prune away any damaged plant parts and then feed it with a half-strength solution of liquid fertilizer. This will encourage additional new growth and, hopefully, flowers and fruit.
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