Is it possible to audit query results in SQL Server?
You could (a) force data access through a stored procedure, then (b) that stored procedure would dump the results to a #temp table before returning them to the user, then (c) the procedure would log the results to some background auditing table.

You'd want to rotate that though because it's going to get very big very fast, not to mention this will not exactly make queries faster. - aaron-bertrand