There is no one answer to this. It depends on the restrictions that have been added. http://law.justia.com/cases/new-jersey/supreme-court/2014/a-94-11.html
While any state may have their own 'rules and restrictions', ponder the idea of Unconstitutional issues. Now the legal argument of ex post facto has its basis strongly backed by the US Supreme Court. While you can not retroactively apply a new law to the past, what would a death penalty judgement legal in the past, if now abolished as a method of punishment create? Consider someone who may have been executed at 12:01 A.M., and the law is changed or abolished at noon? Individual state jurisdictions do not give them a right to be unconstitutional. Look to the ACLU website for in depth information.