[Skarg]

I've played large amounts of combat-heavy games with single players, (even in The Fantasy Trip, where there are no defense rolls, and armor reduces your DX as much as it protects you, and death is at 0 or -1, and there is very little if any magic healing available, and it takes two days of bed rest to heal each point of damage not healed by first aid) without undue PC death or constant hospitalization.

The main things that I find work without forced balance and gameyness such as having the universe magically provide only opponents callibrated to lose have been:

1) Have the player learn combat tactics, in sessions where the player is told to expect to lose a lot of characters. e.g. Do some sample arena combats, or simple sample combat games, or "funnel" adventures, or whatever, until they learn what tactics work, and what gets you killed. Have them learn the importance, possibility, and ways of avoiding or greatly reducing getting seriously hurt.

2) Don't restrict the player group to only one PC. Let the PC join others, make friends, earn comrades, recruit or hire helpers, or run multiple characters (then if one does get badly hurt, they can rest while the other(s) do things) etc.

3) Encourage appropriate caution.

4) Accept that getting wounded some times, and healing, and having to stay alive in such situations, is an interesting part of the game.

And also, though it really doesn't come up a whole lot, except for the weaker NPC comrades:

5) Accept that the risk of death and serious injury is also a vital and interesting part of the game. If you expect to always survive, and not to have to figure out how to avoid death, and really have that be at stake, then you're undermining most of the challenge, interest, logic and point of the situations supposedly in play.