Java is not "Owned", it is open source. If you find a bug in it that you absolutely cannot deal with, you CAN fix it. (There are both open source and closed source implementations, however)
I don't know if you can get the source code to C#, but since Mono copied it there IS an open source for that as well.
I don't know if there is a second source for the .net libraries.
As for the actual "Dangers" (Which was your real question, after all), it would be that the company decides not to release updates any longer--if they do, will the language wither and die or will it take off on it's own? Java is in the process of transition from one of these states to another. Sorry, don't know about C#.
There is also the (Perceived) danger I mentioned earlier about--can you fix it if you hundred-million dollar company absolutely needs it fixed in order to continue.
This was a more significant problem twenty years ago, these days the fact is that if it's a good stable language, this isn't something you ever need to worry about.