Let's introduce you to the world of "Section 3C Protection"! There is a lot more detail in
this UKBA document, but in a nutshell, if you make a visa application in the UK during the validity of any existing visa (NOT after its expiry!) and the application is not decided before the expiry date printed on the old visa, then that old visa is "treated as continuing" until they decide upon the application, and indeed if it is rejected, until the time for appealing against that rejection has expired, and longer, if an appeal is submitted.
Anyone having problems with an employer might want to refer them to the document I link to above.
Treated as continuing? Yes, whatever that visa is. If if for example it is a student visa, then that student visa is "treated as continuing", with a 20-hour working limit during term-time.