Great question! I think when people believe that all social care systems will collapse without the government, they are buying into a very colonialist idea that human beings are at their most basic level selfish and irresponsible and won't care for their communities. This is not the case! Thousands of years of human history prove this not to be the case, and so do the behaviors of humans right now during moments of crisis.
Look to the people of Gaza -- they are not leaving their disabled behind. People are sacrificing all that they have to care for their elderly relatives, neighbors, and friends. The only reason that disabled people in Gaza are dying is because the region is being deliberately deprived of resources by Israel. If aid were let in and the Palestinian people were free, they would feed their hungry, treat their sick, supply insulin, teach children, and perform everything that we currently in the US rely upon the government to supply.
Another example of this can be found in how humans respond to natural disasters. Rebecca Solnit's book A Paradise Built in Hell is a beautiful read on this, following numerous real-life disasters across the globe. In every case, people did not riot and pillage or dissolve into violence--- they formed stable encampments, doctors and pharmacists worked their jobs without pay, cooks made food without expecting a wage, everyone pooled their resources and looked after one another.
We also see examples of this when other governments have fallen -- and all governments eventually do! When a nation-state ends, life doesn't end. People keep going to work to make the medicine and put on the leg casts and wash physically disabled people's bodies and make the food. People WANT to feel useful, helpful, included, and looked after, and they will do these things without being forced to by an authoritarian power structure. We see this in the campus encampments and the incredible outpouring of generosity they are experiencing too.
It is quite common for a person to mistakenly believe that the government is all that is keeping our social order working, and that we are all just one moment away from violent chaos and deprivation without it. But that really isn't true. Even without the government, we will still have the *people* who understand how food production and logistics work, the *people* who research and test the drugs, the *people* who watch the children and nurse the elders and fix the roads and butcher chickens.
Without the alienating, exploitative economic structure we currently have, it would actually be EASIER and more efficient for us to take care of one another with these skills, because our time wouldnt be wasted on bullshit jobs that don't contribute to society.
There are lots of great readings about all of this on the Anarchist Library, but I recommend starting with David Graeber's books! Bullshit Jobs, then Debt the first 5000 Years, then Utopia of Rules, then Dawn of Everything. Bullshit Jobs is the easiest read.