The government can easily save private companies. But should they? I don't think they should involve themselves in saving a private company. However, they certainly can save private companies and have the means and money to do so. All they have to do is fund the company in hard times and the company is saved.
If a private company is floundering, it is almost certainly due to cash related issues. The government is completely capable of infusing more cash into any struggling business. The government should only do this when there is a vested interest in keeping the company afloat. Also the company has to be salvageable otherwise it is a wasted investment the government should not make.