Earlier this month, SHB 1997 was passed by the House.  Under the bill, instead of ending stadium taxes when the debt is paid off, they would be used for arts and heritage programs, affordable housing, community development, and the Washington State Convention Center.

Via Politics Northwest, here is a very useful chart from the Office of Program Research.  It's a timeline of stadium funding, and shows the revenue streams, what they were meant to do, and what would happen to them if the bill is enacted.