That’s strange. I ran DeleteSmallComponents and then ImageAdjust on every example image built into Mathematica and it seems to always produce a Black image.
Does it work for you if you use this example image?
ExampleData[{"TestImage", "Mandrill"}]
If so, then I’d guess there’s something special about your image.
I’m assuming you are working with the images that were discussed in the context of the DeleteBorderComponents question. I’m not able to reproduce the problem you see. For example, using the attached binary image obtained via:
im = Import["jqa_v12_p01.jpg"]
binary = MorphologicalBinarize[ColorNegate[im]]
If I call DeleteSmallComponents with a small threshold, like 300, you can see that lots of the little speckle components are deleted.