Well... we will call this one woosh.
First off lets make a distinction between insurance and Socialized healthcare.
Insurance everyone puts money into the company according to their medical history and risk assessment. Then everyone who paid into it gets what they need. In this way assuming that nothing unexpected happened higher risk people pay more and get more and are protected and the lower risk people pay less and get less yet are still protected.
Socialized healthcare everyone puts their money into the government based on how much money they make. Then everyone no matter how much they put into the pot get what they need no matter their risk or if they put any money in at all.
Now what you are describing takes place in both situations... you break your leg and the money that you have already paid to the government with socialized health care or the insurance provider for insurance and either way your leg gets fixed because you have paid for it basically in advance. Also because you are younger and most likely have less risk you probably have paid for your broken leg several times assuming you have a decent job because you have to cover other people who suck at making money or bodies are fucked.
Now in the case of the retard who has officially become a ward of the state he will no longer pay taxes. This means that he will be getting everything he needs FROM THE STATE. When it comes from the state the tax payers pay for it whether or not he is a tax payer or not.
If you are not paying taxes and you are getting benefits other people are covering you costs and your argument makes no sense at all. When you say lock him up and never let him out you are asking to pay for his incarceration and treatment for the rest of his life and no matter how you wish to sugarcoat it you are the one paying for it.
Thank You!!