It probably depends on your MSBuild / MSTest settings, especially for a gated build (which can do different things in different ways), but hopefully one of the following might at least offer you some hints ...
Test results are usually deleted in the server build folder (not in the drop folder, but in the working folder, in which the MSBuild process stores and builds all the source code, etc.) using datestamped filenames for each of the test runs you performed.
However, it looks like your folder is empty, which indicates that you are looking for the wrong place (if you are doing a gated assembly, it may use a different working folder than the regular assembly, perhaps the C: \ Builds \ 4 folder is next) , or test results are not generated (disabled or not working).
I would try to find the build log, as it will almost certainly tell you what happened to the tests, and if / where any results were written.
If you can find the test result files, you can simply double-click the main test result file to load the test results in Visual Studio (to display the test results in the user interface) - so programmatically you should be able to simply Process.Start(testResultsFilename) to run Visual Studio to view the results (while VS is installed on the computer on which you are using your tool).
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