Ex bullied kid here. From ages around 8 to 14, though it was the worst when I was 8-10.
Context. It was a time when I was abandoned by my only friend at school, had nobody to talk to, no support from my parents whatsoever. I was scared of everyone, socially anxious to the point when I couldn't talk especially at school. I would get in trouble for not speaking in class when the teacher called me up, because I was so terrified of everyone. I was basically one of my schools' scapegoats, laughed at directly and behind my back and I was seated by the teacher with my worst bully for a whole school year because "I was so calm and well behaved and thy needed someone like me to be an example for a naughty kid like him". I was terrified of going to school, unable to eat in the morning when I had to go there, couldn't sleep. Fun things. It got a bit better when I got friends around the age of 10, but we were still "on the bottom of social hierarchy" in our school. Me especially because I was terrible at sports and looked sickly skinny which was a "great" material to make jokes of.
I was convinced that I'm a worthless piece of shit, bad at everything, not deserving of anything good. I know I'm not a very extreme case (though I didn't mention MANY details here), I was a lucky mf because I found people who kinda helped me get distracted sometimes.. you know, my group, people who accepted me though looking back we weren't really that close and I couldn't talk to them about many things. I was also always quite creative and started writing stories which kinda saved me because I had this another world to turn to and also realized that I can be good in some things, maybe.
Anyway. Over time things got better. First I started accepting the fact that it's not me who is broken, these kids are just jerks. It was hard to overcome some "automatic" behaviors and thoughts, like for a very long time I had a problem with maintaining relationships because I was convinced that everyone secretly hated me and I didn't deserve to take up anyone's time. I remember that when I was in high school I felt like all those experiences "broke" me, thought I would never be able to form any close relationships with people. But it changed over time.
I went from a terrified 24/7 kid who didn't speak to anyone including his family (even though they weren't bad), locked myself in my room for entire days, spent like 70% of my time holding back tears and the rest crying... Etc, to - I guess a functioning adult, still with some problems and getting episodes of "ohh no I don't deserve anything good" but overall, it's.. quite okay. I'm not saying I'm the happiest guy in the world (I wouldn't be in on this forum if I were) but I think I mostly got over the thought patterns that bullying got me into. I can talk to people, some even consider me very sociable. I had some time in my life that was quite good. Then everything faded away, but.. that's another story.
I still have depression which is PROBABLY somehow related to what I've gone through but eh, it's probably mostly from other things (also literally over the half of my family has mood disorders. So.) Also I didn't get any kind of psychological help/therapy until I was 20 so I would say I went through these things by myself. I would say that with a help of a professional, breaking these patterns would be a lot easier and maybe faster.
Anyway I would say I'm in a decent place in life, and those past events don't affect me too much. Other things kinda break it but it's still okay.
So tldr yes, bullied people can survive and have a decent or even good life. I also have friends who are like that. You can go through terrible things and move on, I'm not saying it's easy - but its certainly possible, one thing at the time.
Good luck <3