As a MF agent who spends a large amount of time calling apartment owners (or rather, numbers purporting to be apartment owners), please believe me that reaching out to random run down buildings owners is unlikely to get you any deals. Finding the correct contact info is hard enough, but if your pitch is that they should sell cheap now, you're misreading the market.
Multifamily properties are worth significantly less now than they were just a few years ago, and asking for a further discount due to property condition would probably result in a loss, maybe not even pay off the debt. Their clear incentive is to bet on falling interest rates between now and debt maturity.
A small handful of owners are forced to sell due to a looming balloon payment that a refi won't cover, but you're not going to find one of those by driving the market when any commercial broker can just look up properties on that basis and start making calls.
I would also be careful talking to property managers - they may have no problem telling about "other" buildings, but change of ownership in their own building is a threat to their livelihood. Not to mention, they probably won't want to admit it if a building they manage is in really bad condition.
If you're serious about buying you should first talk to fellow investors and define your buy box. For commercial buildings, be very specific - price range, $/door max, unit count, unit mix, part of town. When you can communicate both your strategy and criteria (and are financially credible), you can leverage your network and get meetings with brokers who are willing to shop for you.