As an agent in the Matteson area I can say that Contingent, pending and A/I (Attorney & Inspection) mean that the seller has accepted a contract. The parties should be moving to complete terms of the contract like loan applications, home inspections, attorney review etc. Agents are required to present all new offers to a Seller as soon as they receive them even at this stage. Here in Illinois one type of contingency in a contract where a Buyer has to sell their existing home prior to closing on the new home might be able to be "bumped" for a new contract under certain circumstances and terms. It's probably better for a Buyer to concentrate on properties that are on the market. We have automated searches that will email you Listings that meet your specific criteria directly from the MLS in real time. Feel free to contact me if you wish and I'll be glad to help.
When a property is pending/contingent it means an offer has been accepted by the seller and there are contingencies still in effect (i.e. appraisal, home inspection, loan, etc.). Some sellers will accept backup offers in case the current deal falls through for some reason - and, some seller won't. If there is a property you are really interested in, have your Realtor contact the listing agent to see if the seller is accepting backup offers.
You might be able to place a backup offer on these properties; or just find one that's active and still on the market for sale.