Getting the percentage of a result set for same ID rows
The datatype of a COUNT is a [BIG]INT and integer divison results in truncated values, either zero or one. Multiplying this times 100.0 returns  either 0.0 or 100.0, so you just need to change the order of calculation to multiply first:

100.0 * COUNT(CASE WHEN ou.OutcomeName = 'Death' THEN c.CaseID ELSE NULL END) /COUNT(c.CaseID) AS 'Death Events',