I have done it both ways , collected my bags for a 24 hour layover, and checked them through to the final destinantion.
In both cases the agent at the counter asked me where i wanted my bag checked to, the final destination, or did I want them in SIN and then re check them the next day.
If you have a problem and they make you claim your bags , you can always leave them at the luggage storage desk, i can't remember the cost for that though.