I think this was a question on a MBTI test or something. I've always considered it such an odd thing to ask! To ask someone who is gazing far of into the distance if they identify with broken, discarded things...

I would think it's obviously an INFP + E4 thing more than anything else. But the question could be also be asking if you feel sympathy towards such objects, and perhaps there are other interpretations as well.

For me, the question invokes many things, but at the highest level, it represents Life itself and its difficulty at getting up in the mornings sometimes.