Since the concentration of your stock solution is 1000 mg/ml , if you take an aliquot of 10 ul, the concentration of the solution remains same unless you further dilute to a certain volume. But the content in 10 ul will be 10 mg only.
An aliquot volume has the same concentration as its original solution. So it is still 1000mg/l and may change only by dilution or concentration process.
The concentration should be the same since the aliquots are not undergoing any further dilution. The principle is that any part thereof of any concentration will have an identical concentration to the original stock solution.
The concentration (w/v) remains 1000mg/ml, however the mass of solute in 10μl aliquot is 10mg. i.e 10ml solution contains 10,000 mg; 10μl = 0.010ml will contain 10,000 mg/10ml x 0.010ml =10mg.