The answer rate is what you want to look at if you want to see a numerical representation of
a users
"no answer selection attitude".

However it might not always be correct to take this measurement at face value
You would have to consult each user on each question to confirm that they are actively and maliciously not voting or accepting an answer. :P
But on a serious note - you really have to read into each of these posts that the OP did not act upon.
Some sample conclusions from reviewing all of a users posts -
- The user simply hasn't been back to the site.
- This can be frustrating at times. Remember that there is a real life world out there beyond out little haven of knowledge that we have found here. Once you have that coveted fanatic badge and have already screwed your visited/consecutive days rankings, you might go AWOL for a few days to clear you thoughts. You know... Zen style...

- Sometimes (depending on how long ago the post was) the OP might not feel that he has received enough attention on his/her post and wants to let the question trickle down from the fastest gun's in the west to the hardcore bounty hunters.
- Sometimes the OP genuinely finds that none of the answers that he was provided assist him in anyway - lets not rule out this possibility.
In addition, the system provides a reminder for users that have posted questions and not yet accepted any answers after a certain time period. A banner like structure hovering in your profile view..
I believe that this might only be triggered if one of the answers has a positive score... Yet to be confirmed...
TL;DR
yes - There is a mechanism in place. It doesn't punish the user per se, but rather reminds them to consider accepting one of the answers that were provided to his/her question[s]. Some users find it rather annoying so that might be considered some type of punishment :)
/M?S[O|F|U]/i has it all... and then some...
@
to notify him.