If you got hit by a bus and became disabled or just some old age related thing, it's still the same. You got unlucky, life screwed you right up the ass. Again, human compassion is of course a feature of civilized men - but at the same time, it is not society's duty to reverse the iniquities of fate, nor is it right for this duty to be pushed upon it.
What you describe is no different to me from, for example, the states appointing a free colostomy bag changer to all incontinent old farts. Sure, it's a sad misfortune, but the brunt of the cost is for private citizens (the person's family, charities, churches, insurance companies) to bear, voluntarily (although in some cases they can and should be shamed for failing to). It is not a public matter for the state to meddle in. If an old man has failed to rear good children who take care of him in old age, has failed to make friends who will help him, failed to plan for his retirement and insure against these problems, private society has failed to create charities and such to help those in need, then government should not bail him out.
Among other things, this also contributes to strengthening family ties, instilling foresight in citizens, and generally promotes a cohesive, stable, healthy society.
The exceptions I would grant are:
The military should be expected to contractually promise servicemen that if they are disabled in their service, they will be taken care of. They shouldn't be required to do this, but failing to should generate enormous societal backlash since it is outrageous jewery. Not to mention nobody in their right mind would volunteer without such a guarantee in a non-welfare state, taking care of disabled veterans should be a personnel cost factored in by the military's budget.
Same as the military, should be an accepted and expected contractual clause. Again, no mandatory requirement, and unlike the military there are multiple companies so some will doubtless refuse to make the guarantee - these should be looked down on as predatory by the people for this (although not as much as in the case of the military, since anyone who doesn't like it can go work for the competition), and they should offer typically higher salaries (as consequence of market forces social mores, not law) to adjust for cost of insurance against possible maiming that employees will want to buy.
These people are not numerous, so supporting them is a trivial cost, but setting the athlete's mind at ease against such a catastrophe will help them focus on their sport and also encourage the public to strive for athletic achievement by making it a better quality career.
Or for the small government option, social attitudes should be such that insurance companies start offering free insurance packages to such people, in exchange getting public goodwill and free publicity (similar to current equipment sponsors).
Even this last one is optional although I feel it would benefit a stable society. However, ordinary people (and unborn fetuses) should not have a blanket guarantee against misfortune from the government. That is just stupid, the only argument for it is basically heartstring tugging.