Why Does Image Deconvolution Still Work with Image without Sharp Edges?
Think of it in the frequency domain.
Some of the data is highly damped.
Namely energy in High Frequency is damped with low values.  

Yet, unless it is zero identically "There is hope...".

Basically, this is the idea behind deconvolution algorithms.
Restore the energy in frequencies before it was damped.  

Practically, we are limited in DR.
Namely if it is damped really hard, even if it not zero, in order to restore it one would amplify it significantly which will also lead to noise.

Regarding the edges, well, assuming we have the right way to recover the enrgies edges will be restored.