Because sometimes you want things to look like a crappy, blown-out xerox. Or at least one person on /r/adobeillustrator did.
- click on the circle to the right of the layer with your b&w image to target the whole layer for effects
- open the appearance palette
- effect>stylize>inner glow (set it to white, 100%, probably a pretty large blur)
- click on the effect names in the appearance palette to edit them
If you don’t want texture in black areas you’ve drawn over white areas then do a bunch of Pathfinder to make it just white shapes.