so... I've never been really poor, but like most of us, I've had lower income and higher income. Everyone gets unexpected bills, but my experience has been that those bills don't get larger with your income (even though most of your expected bills do grow with income) - a lot of those unexpected bills get smaller in absolute terms as your income goes up; both cars and medical expenses, in my experience, tend to move from 'unexpected bill' to 'expected bill' as your income goes up, as you generally get much better health insurance and newer cars.
But even the things that don't move from unexpected to expected are harder to deal with when you are poor.
Example; person A makes $14K/yr at walmart. They put away 10% of that every month.
person B makes $200K/yr at Facebook. They put away 10% of that every month.
Say you get a $250 parking ticket.
If you are putting away 10% of your 14,000/yr salary - that parking ticket is gonna be a pretty big bite of your savings. I mean, if you've been putting away $1400 a year, you can cover it, but that $250 is still a big bite.
If you work at facebook... say you are still putting away 10% of your $200,000 salary - that parking ticket costs you just as much, but it is a whole order of magnitude smaller when compared to your savings rate.
Medical expenses are the more common case for unexpected bills; it's super expensive to get hurt while poor. It's not so expensive to get hurt while wealthy.
Say you are playing catch with your kid nephew and you fall and mess up your knee. If you make $14,000, you probably have health insurance with the maximum deductible, and end up having to pay a bunch out of pocket. the 2019 out of pocket limit for an ACA compliant HDHP plan is $6750 - that's going to take a lot of saving 10% to pay off. And even if you do get it fixed, you probably have a job where you have to stand up and carry things; you will need a bunch of time off, time off that you're not gonna get paid for.
Say the same things happens to the software engineer making $200K/yr. First, that job probably comes with pretty nice health insurance; you probably aren't out much out of pocket at all. The place where I work offers a HDHP plan but they actually give you an amount of money equal to the deductible every year. (me, I still take the traditional plan, 'cause I'm willing to pay extra if I don't have to deal with medical billing at all) Next? SWE jobs usually come with a bunch of paid time off. This person probably gets paid to recover at home. And if they felt like they needed to work? they probably could work from home; and for that matter, their job probably doesn't involve knees much, so they are gonna be able to go back in to work much sooner than the guy working at walmart.