As a landlord of several small homes (and therefore in close contact with my tenants) I can only suggest this:

Do what you can to stop further decline in your credit. Every month counts (some creditors, like CC's or Loans show monthly payment history, whether it was on time or late by 30/60/90 days, etc.). Do not allow small items like cell phones, Cable TV or Video Rental to go to collections. If it has, get it paid off. (I have seen that on several applicants' reports, and to me, that looks bad, like a person is running around using non-essential type services, racking up charges and simply not paying for it.) I never look at Medical collections, because my own personal take is they can screw up billing easily. (I have excellent credit and once had a large urban hospital send my first surgical bill straight to collection while I was in that same hospital 21 days later having a second surgery w/admission. Discovered the first bill went up for collection upon my discharge, had to get a ride to the collection service to get that one straightened out, when I was supposed to be at home in bed.) Do what you can now to start showing improvement in your credit and remain consistent with it each month.

As a landlord, I take a close look at that. I just rented to a nice young couple who had to file bankruptcy about 4 years ago. Stuff happens in life and a sudden illness or catastrope can send us into a financial tailspin. However: if their credit shows good records after the financial crisis, and stays that way, I have no qualms renting to them. My young couple's credit was good post-bankruptcy, they kept a low ceiling on a single credit card, had nothing go to collections, so they were establishing a good track record. Some of my best tenants have been those who got in a jam when life blindsided them, but they found their way out. With that said, I'd encourage you to look at smaller units where you have direct contact with the owner/manager. Don't hesitate to tell them a separation hurt you badly. (Landlords are human too and many have had bad experiences in life.) Be straight with them. As a landlord, the person that stands there and makes lame excuses or blames it on errors (oh, they said we didn't return all those videos, but we did, and that credit card kept messing up our bill, and that cell phone charge was a phone I got for Aunt Susie for Christmas and she never paid the bill and I didn't know about it) etc. I have heard those things said and pretty much tune them out from that point. They've lost. Why? Because they refuse to admit responsibility for their actions, have an excuse for everything and it's usually always someone else's fault. That shows lack of maturity, responsiblity and self-discipline to me so they probably aren't going to take paying their rent too seriously. But the person who is honest and says "Look, I know this looks bad, but I went through a really bad divorce and lost my house and things got rough for awhile so I had to file bankruptcy. But I'm coming out of it now, I'm really trying. I have one credit card for emergencies and keep the limit low, I pay for purchases in cash, I'm really trying". If their credit history is parallel to what they tell me, I'll listen. If you apply to large complexes only and get caught up in a big machine that has little flexibility, I would think your odds of 'being heard' would be slim.

Good luck, keep your chin up!