Supposing there are a Jewish man and woman who are the only survivors of a crash landing near a deserted island, and their respective families have written them off for dead. Over time as they struggle to survive, they fall in love. According to a previously answered question they cannot have a full Jewish marriage due to lack of witnesses.
This question asks: Can they contract any lesser type of marriage? Or does the Law strictly require the pair live chastely until they die of old age?