Several ideas have been discussed related to this issue. The official ruling from Rob Daviau at Hasbro is that they are "dead cards" and worthless.
Some gamers have suggested that: (1) you should be able to play any card (not just Combat Cards) rendered useless by the death of a minor character to heal your major character, or (2) healing works exactly as described in the rules, except each minor character Combat Card is worth 2 points of healing, or (3) playing minor character Combat Cards as healing doesn't cost any points, but remain worth just 1 point of healing. Another suggestion was to eliminate healing altogether and to allow players to discard up to three minor character cards and draw three new ones, at a cost of two actions (an entire turn).
I've always played by the official rules and don't see a particular problem, but some of the suggested variants look interesting.

