signal sampling for 2nd time of sampled signal
thirI believe it is a nonsensical question, or at least a tricky, meant  to detect students who have  a shaky knowledge, and whose anwser deserves a lot of care.

First trick: if the $600$ Hz signal is sampled at  $1000$ Hz, it will endure aliasing (a proper sampling frequency would be above  $2 \times 600$ Hz). If the sampling process is perfect, it will appear as a sine at the mirror frequency $2*\frac{1000}{2}-600 = 400$ Hz.

The  signal (that is assume real)) is now  in the $[0,500] $ Hz band. An ideal-low pass cutting at $500$ Hz would thus be an all-pass, second trick, and would be utterly  hard to design, numerically, in that case (third trick). 

So in theory, the  output signal would be the same (aliased) signal as the one from the first stage, fourth trick in a way.