It is not necessarily claiming your sister as a dependent, but the actual circumstances that may affect SSI. For example, when another person gives you shelter, food, and pays most of your living expenses, SSI can be reduced. So, if you don't claim her as a dependent, but you pay for her expenses and she lives with you, you still have to disclose this. Here is a link to information about this topic:
If she meets the dependency tests for you and she has no other income than SSI, you may claim her as a dependent.
You would have to pay for more than 1/2 the cost of her support to claim her as a dependent for tax purposes. If she is renting a room from you, you might not meet this requirement. I cannot tell you if claiming her as a dependent will make her lose SSI--I only know that the circumstances are what are considered. I do know however that being a dependent is not expressly prohibited for persons who receive SSI. Have you tried calling the social security administration?
If you claim her as a dependent, it is presumed that you pay more than 1/2 of her support. This can be taken into consideration when determining her benefits. Here is a question that might help: