You appear to have unearthed a bug in 5.11 (and perhaps earlier versions). To work around it here's a convoluted procedure...
1. Select (highlight) the clip that's to be faded.
2. Right-click on that clip and SAVE AUDIO CLIP AS NEW FILE. It will appear under the audio tab in the media area.
3. In the preview window, right-click on the audio display and apply the FADE OUT.
4. Click the original audio clip on the timeline and use the ||< and >|| keys under the preview window to align the scrubber (red line) with the start of this clip.
5. Click on the new audio clip in the media bin. On the bin's toolbar, click the chevron just to the right of the green arrow. Click the OVERLAY SEQUENCE AT CURSOR choice.
That should place a duplicate of the audio clip directly under the original.
6. Right-click the original audio clip on the timeline and click UNLINK FROM VIDEO.
7. Right-click the original audio clip on the timeline and click DELETE.
When the sequence plays it will switch from channel 1 to channel 2 audio at the start of the clip in question, and it should fade out.