I need a better explanation of the problem?
Are we talking complete collapse, no return? Are we talking worst parts of the bible? Are we talking like 1984? Where on the spectrum of hand full of dust to oh god oh god I dropped my iphone are we at?
The reason I ask is simple.
Your goals for short term and long term survival is completely different.
If it is short term, less then 3 months with out law and order. It really will not matter. As long as you are not part of a very large group or follow the group collectively jump off a cliff, you will be fine.
After three months, being alone will kill you. Being in a smaller group will get you more time, but humans are conditioned to have small societies of 300-800. We simply don't function well as a group with smaller numbers. We have a tendency to get little dictators that start to exploit the system for personal benefit. The lack of a counter voice and protection for that voice is more dangerous then disease in small societies.
As for how many and who you trust that is up to what who you are.
If you are very religious, then you can more or less trust the members of your church to stick to church rules, or expect them to punish each other if they are not. But rules are fluid and this can come around to marrying young girls and burning witches very quickly. If you are willing to follow the rules set by the leaders, you are good. This is how society has gotten along for thousands of years with out a major society to rule them. Religion was used mostly to replace societal laws when enforcement could not be expected. This works up to about 50-80 people. Then the counter voice will get frustrated enough to give the starry eye mosiah a violent farewell.
For larger groups, you can set up a communism/direct/indirect democracy system.
Everyone gets a vote and no one is placed in the solo/compete ruler role. yes there is chiefs, but they where more of public figures and negotiators then rulers. For example, the Cheyenne elected 4 chiefs from each band that held congress. The ten bands would get together to elect the arrow keeper, which is elected by all the chiefs in the congress. Any change for the system would be a vote by all the people relayed to the 44 congress chief, that would vote on their behalf. Any rule that needs to be enforced would be done by the arrow keeper. All decision that required direct military response or dealing with outside bands was done by the arrow keeper. When the counter voice gets tired of the current problems, they elect them out.
Sounds familiar? Yea. Our system of government was invent by the natives (more based on the Iroquois) . For the most part, hunters and gatherers have done this for tens of thousands of years. It works. It does require everyone to know their place and believe in the system. But it does work.
In really bad environments, you can do the Aboriginal Australian version. Small groups of less then 10 people that come together and separate when needed. It is very hard to keep large groups of people live in most of central Australian, they they develop a cultural response to it.
But to go back to the answer.
Yes, no, maybe.
If you where the only person left on the planet, you would live to 30ish? If you are lucky, 40ish?
A small group between 300-800, life expediency could go up to 50-70ish?
Given the ultimate goal (of all life) would be to reproduce, and genetically, you need 500 to 1500 people to do that.
With out others, a 50 year life with out reproduction will feel like a 300 year life and genetically a failure.
If reproduction is the main goal, you need at least 500 people.
If survival with out dying by unnatural means is the main goal, then you can do it with maybe 10 people. But you are considering dying by infection at 40ish years old a win.
Remember most of your deaths in this case will be from infection and other natural causes. You will fall down break your leg. You will get an infection. You will get sick. With out others you will not survive.