In my experience, short term help is available fairly easily. It’s after the day or two has passed and you’re still broke and unemployed that’s the problem.
In my 20s, I quit my job, fed up with asshole boss. I had nothing lined up, just a bit of savings. My lease was up so I dumped everything in a friends garage and moved into a $10/night SRO. It was an 8x10 room with a twin bed, chair (with obligatory stuffing coming out) and 4-drawer dresser. I spent $15 on a used mini-fridge, $25 on a used microwave, and $30 on a used portable typewriter. I budgeted about $20/week for food and set about writing the Great American Novel (“The Cain Principle” - I still love the title). After writing the first 200 pages about 5 times, I started looking for a job, and found something a couple of months later, with weeks to go before my savings would have run out. I wound up staying at the SRO another year - my expenses were so low that even with the crappy job I found, I was able to rebuild my savings back up. Once I was promoted, I found an apartment and rejoined the lower-middle class. 
I followed the pattern of most people. Meals were noodles or rice with tuna mixed in or generic oatmeal with raisins (still a favorite breakfast of mine), entertainment was books from the public library, clothes were from thrift stores.
Why would you take on a refugee family if you’re already having trouble making ends meet?
Back in the day when I was getting my business started, I was also in this nasty lawsuit with my former employer. It was bad, I did not have the money I needed.
Our mortgage would go 3 months late, we would get the foreclosure documents in the mail, start getting these nasty documents in the mail from the bank’s attorneys. Then money would come in, I would pay the mortgage up to date. The bank had to take the payments provided I paid the entire amount to bring up to current. This happened to us 5-6 times over 3 years, or so.
It was interesting that I actually got on good speaking terms with the lady in charge of the foreclosures at the bank. I knew she had to do her job, and she knew I always paid up but they had to go through the process each time.
Then the lawsuit was over (I won), things got well in the business and it was all behind us. To this day I keep all the mortgage, car payments, and electrical accounts paid up to 6 months in advance.
Reading this thread is a good reminder that I may have been broke many times, but I’ve never been poor.
I think the basic difference is that when you’re broke you become ingenious; when you’re poor you become desperate.
I think a big factor is debt. It’s easy for people, including poor people, to live on borrowed money to tide them over what they assume is a short term situation. But if the situation turns out to be more long term than they expected and the debt comes due, they’re in a much worse situation then just being broke.
Absolutely, Little Nemo.