Operating system: Windows-10-10.0.17763 64 Bits
Graphics card: GeForce GTX 1080 Ti/PCIe/SSE2 NVIDIA Corporation 4.5.0 NVIDIA 430.86
Broken: version: 2.81 (sub 3), branch: master, commit date: 2019-08-26 20:39, hash: rBce2368cf69f5
Short description of error
Export selected object export empty file if object have only mesh selected in outliner.
Exact steps for others to reproduce the error
Probably this is more UX bug than exporters problem.
Create default object: Cube or Suzanne.
Expand Object tree and select mesh in outliner. Blender will switch to mesh edit mode.
Click one more time to mesh in outliner. BLender will switch to Object editing mode.
Viusually Object still looks selected because mesh still highligted but in 3D viewport object is unselected.
Now try export as OBJ, enable Export Selected only.
Blender correctly will export empty OBJ file because there is no any object actually selected.
This UX bug quite confusing, and i catch it almost every time i need export files.