I have to say that the Eleventh Amendment was not the first thing that sprang to mind after the disaster at Virginia Tech. But apparently Virginia's thinking about just that - the state's (oops: commonwealth's) solicitor general, William E. Thro, mentioned that the state would invoke its sovereign immunity to prevent suits in federal court. He also mentioned that people could sue in state court, but could get no more than $100,000. Link.

Thro (who, I'll note for the hell of it, went to U. Virginia for law school, has an M.A. from the University of Melbourne, and is an Eagle Scout) is presumably referring to a state statute waiving its immunity from suit in its own courts for negligence, but only to the extent of the $100,000 that he mentions. A quick spin through Westlaw turns up no statute, but I didn't look very hard.