It's a shame that fasting has been eliminated from the culture, but i guess that's what happens to things you can't make money on.
I have fasted many times for that length, and I happen to already be thin. Never even got close to refeeding syndrome.
I've read a variety of books on the subject. I've spent some time on PubMed. I don't know everything about fasting -- absolutely not -- but I know enough to say that you might be misremembering the time it takes to get refeeding syndrome.
I personally believe the number is closer to 30 or 40 days. We are talking Christ-level fasters, hunger strikers, performance artists, or concentration camp victims.
I downvoted your comment because I consider it to be spreading misinformation, and because your tone indicates that you have expertise or experience on the matter.
Say I'm 192cm and 69kg. My BMI is 18.7, which is definitely low, but perfectly healthy. I have an active lifestyle and burn 3500kcal per day. If I fast for 7 days without changing lifestyle, I lose roughly 7*3500/7700=3.2kg of bodyweight. By that point my BMI is 17.9. According to this paper[0] with 632 citations, anyone with a BMI <18.5 who's not eaten for more than 5 days is at high risk of refeeding syndrome.
If you think the numbers are fictional: those are my numbers from ~5 years ago.
It is rare that eating after fasting causes critical illness. Just check online. People do this stuff all the time.
https://www.hopkinsmedicine.org/gim/_pdf/consult/refeeding_s...
Most Americans could go weeks without eating, and they'd be mostly fine.
Sudden refeeding is an issue, of course, because of electrolyte balance.
But we have a misunderstanding of how long the body can go without food, by design.
What we mainly need is water during periods without food.
After about 3 days without food, the body stops telling you your hungry and switches to fat metabolism.
You need electrolytes for sure; but unless you've recently been prepping for a body-building competition, you don't need any calories for quite a bit longer than that. I did a week-long fast for religious purposes many years ago, before the whole IF health craze was a thing. All I had was water, and occasionally some salt. I still had plenty of fat at the end of it, and I wasn't particularly heavy before.
According to the book I read at the time (again, focusing on fasting for religious purposes), it's only after 3-4 weeks that a typical person experiences a more urgent type of hunger pang, which is the indicator that your body is starting to cannibalize critical infrastructure (and that it's probably time to stop fasting if you don't want to damage your health). People who are actually overweight presumably have enough calories to last for months.
Vitamins and minerals are obviously another thing. You're not going to get a nutrient deficiency in a week, but you might well in a month or two. (I am neither a nutritionist nor a doctor.)
It's the same with fasting: If your body isn't used to fasting, you feel like crap; nonetheless, your body was designed to fast. Take it slow and keep practicing, and the rust will work off all those unused chemical pathways handed down by your ancestors. (Again, if you have diabetes or hypoglycemia or something like that, maybe fasting isn't for you.)