What does it mean by cover; wrap it around or put it between the fibre end and light source?
If wrapped around, you would still see light from the source because light travelling down the fibre is reflected and so would never encounter the wrapping.
If as a barrier between the fibre and source you wouldn't see any light because no light passes the covering to enter the fibre. Total internal reflection can only work on light that comes in (and comes in at very close to parallel to the length of the fibre.)
If the obstacle was, say, a coloured filter then you'd see the colour the filter lets through. If it was a diffracion grating then you'd see light if the fibre is in a bright spot of the diffraction pattern.