"Rescue" = stealing.
Cry me a river ladies. If it's been there for months and it's rusted it's abandoned. You love to flaunt around faulty morality. Use of public space to park a bike is a priviledge, leaving the bike locked for months and not retrieving it makes it abandoned by public consensus and by law (I don't remember the exact criteria to be met).
If it's in someone's garage for a decade it's still property, if it's locked on the street for a decade, it's clutter.
There are usually a bunch of stickered bikes in Hyde Park over at the shopping plaza on Kimbark, on the stretch of 57th between the Metra and Woodlawn, and in front of the Regenstein Library and the Reynolds Club. Not entirely sure it would be a good idea to wander around the neighborhood with a giant pair of bolt cutters "liberating" them, but you might get somewhere with the UCPD if you explained that you'd like to get stickered bikes off university property for a project you're working on.