A punk rocker who does not care so much they look like homeless street lurkers and will eat anything derived from anywhere such as discarded food tossed on the ground or left in the trash.

Crusty punks have no care for personal hygiene at all. The reference to being a Crusty Punk is based on them being so dirty they form a crust of filth around themselves.
Example 1:

I was at the Punk Rock gig my buddy went to and this crusty punk picked up a burger someone threw in the street and ate it.

Example 2:
I'm a crusty punk. I could care less where i find food, I will eat it even if it was in the trash.

Example 3:
Young man, I don't care if you like punk rock. You smell like a clothes hamper full of week old gym socks. Take a shower. I am not having a crusty punk living in my house!
by Fractious1 December 14, 2017
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Me: You're dirty.
Mitch: No, I'm a crusty street punk
by TFH August 26, 2003
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