Question: In the US, which part of the government is holding the money due to federal employees?

During a government shutdown, what happens to this money? Is it reinvested through short-term lending?

Answer: 
From the perspective of the U.S. Constitution, all of the US government's money is in the Treasury of the United States. Money comes out of there and goes to whoever gets it in accordance with legislation passed by Congress. If there is no such legislation, the money stays there.

While it has become the habit of some people to speak as if the Treasury had compartments of money from which money can go only to certain destinations, where this is the case it is a creation of Congressional law, and not anything in the Constitution. Whatever legal barriers exist are the creation of Congress and can be abolished if Congress makes another law.

All of that money that would have been paid out, if the shutdown had not taken place, is still in the Treasury.
To add on to EvilSnack's answer more on point to what happens to the money in the Treasury viz "reinvestment through short term lending". It would be wonderful if that were the case.... Unfortunately there is little to no money to do that with - to the tune of almost $22T in debt. For a more exact reading see <http://www.usdebtclock.org/#> . What actually happens is the Treasury manages debt re-issuance to meet cash flow trying to hold the least cash safely required.