They 'ran out of soldiers' because they were surrendering en masse. It's difficult to know the exact numbers on anything from that era because there are ambiguities and poor record keeping abounds, but it's estimated that some 11 million Germans ended up surrendering. [1]

So yeah as morale collapses you're left expanding the age of conscription, which further collapses morale. There were plenty of sardonic jokes about the Volkssturm, 'the people's brigade.' Why is the Volkssturm the state's most valuable resource? Because they have silver in their hair, gold in their teeth, and lead in their bones.

[1] - https://en.wikipedia.org/wiki/Befehlsnotstand#Nazi_Germany