Something that can't be taken away doesn't mean it can't be suppressed/infringed upon/violated.
Your right to keep and bear arms is inalienable.
If I disallow you from carrying into my place of business, I am suppressing your use of that right; but I am not stripping you of that right. You can leave my place of business and continue to carry a weapon. You can even IGNORE my request, and still carry a weapon INTO my business. I have in no way "taken away" your right, though I have attempted to infringe upon it.
Similarly, the government is unable to completely take away ones right to free speech, to freedom of religion, to the right to bear arms....but they ARE able to suppress it, to infringe upon it, and they are able to do so with the entire weight of the social contract with it is built upon behind them. Thus the reason why the constitution provides a degree of protection to the citizenry from the government engaging in such a thing.
As with all matters of social contracts, there is give and take regarding how much we the individual are willing to voluntarily allow our inalienable rights to be surpressed via a system of laws in exchange for the benefits and protections that a system of government provides to us. But it is impossible, short of death or something akin to it, for the government, or anyone, to permanently REMOVE your natural rights. IF such a thing is possible, it is a good indication that said "right" is not actually a natural, and thus inalienable, right but rather simply a privilege constructed within the social contract.