Can it exist? Should it exist?
All the standard examples (parent-child, man-dog) fail to imagine the very real possibility of abuse. Children can turn into terrible criminals (after all, murderers have parents too), and can sufficiently disappoint their parents to emotionally disown them. (Pathetically, this appears not to have happened to multiple-sex/murderer Karla Homolka and her parents. “She was always a good girl.”) LIkewise, parents can perform abuse from the routine to the awful, which over time can shrink the hearts of children; turn the dominant feeling from love to fear.
As to the normative aspect of “unconditional love”: why would it be such a good thing? One may imagine it as a permanent substrate of a relationship, and infer that it is invincible. Instead of earning it, polishing it, strengthening it every day, one may presume it, enabling an attitude of recklessness. Likewise, from the point of view of the recepient of “poor-quality” love, being told to nevertheless offer unconditional love is tantamount to promoting Stockholm Syndrome. It is not healthy to be uncritical.
As the punchline about the physics of Santa Claus, if there ever was unconditional love amongst the living, it is gone now.