Q. Since they claimed me as a dependent, don't they have to provide me with shelter?
A. No, they do not have to continue to provide you shelter. They only must have provided you shelter for most of the tax year (2016) for which they claimed you.
A more relevant question may be: Can they continue to claim me as a dependent after they kick me out? The answer is: that depends on when they kick you out. They may, most likely (there are other rules to meet), claim you for 2017, if you lived with them for more than half the year.
