Assuming it is SSAS Multidimensional you can deploy ASSP and build a rowset action which returns the right rows. The rowset action expression would be something like:
ASSP.GetDefaultDrillthroughMDX(Tail(NonEmpty(Existing [Date].[Date].[Date].Members), 1).Item(0))
To explain that code, we get the existing dates (the dates in context of the current cell) then we filter down to only dates with a non empty value for the current measure (inheriting all the other filters on the current cell) then find the most recent date.
More info on this stored procedure can be found here:
Note a rowset action can't be the double click drillthrough action in Excel unfortunately. You will have to expose your action when users right click on the cell and choose Additional Actions.
Excel has a double click behavior. Double click performs a drillthrough returning either the default columns or returning the columns you define in the drillthrough action you define for that measure group as default. If I execute a DRILLTHROUGH SELECT statement manually without specifying the columns I want then I will get back the columns defined in the drillthrough action flagged as the default