I know in the US, how much debt you have has zero bearing on your ability to qualify for welfare programs, but savings can negatively impact your ability to qualify. So owing less doesn't qualify you for more aid, but having too much savings can screw you out of benefits in an emergency situation.
Some countries have programs that provide health benefits just because you exist. In the US, a lot of our benefits programs are "needs based," which means you have to qualify for aid and one of those qualifications is that you don't have savings because as little as $2000 in the bank can disqualify you.
I don't think it's as one dimensional as the above comment seems to suggest. But I bet there are inherent incentives in the US to not bother to save for various reasons. It would be interesting to see that investigated in earnest.
When you apply, you basically swear this is true to the best of knowledge and if it isn't you can be accused of fraud and potentially charged with criminal activity, or just have the money taken back in some cases. (My knowledge of the system is limited, but I was on food stamps for a while. Having something like $2000 in savings can disqualify you, iirc.)