They deal with it by being supportive of their wife. If the woman is uncomfortable having sex after menopause and doesn't want to at that time, then they don't push her for it. Men also lose much of their sex drive as they age and testosterone decreases, so typically there isn't a huge difference in sex drives between the couple. If it becomes a big problem, then he should talk to his wife and express his concerns in a respectful manner. She can go onto hormone replacement therapy to help or another form of treatment.
Sometimes if the vaginal tissues get thinner and dryer, sex can hurt or even make the vagina crack and bleed. There are hormone-based creams for this. If pain is your wife's problem, she might want to use the cream for general purposes, and maybe this would also rekindle her interest in sex. Be sympathetic, nothing is a turn-off like painful sex. If that is it, however, she might be convinced to try some solutions rather than give up on sex entirely.