A STR 1 is just above being hospitalized or in a wheelchair. There is no easy explanation for having a STR of 1 unless you have a compelling reason in your back story and qualities to accompany it.. I sit around all day polishing my stuff all day is no reason. Just doing that you would at least have a STR of 2. The only reason to have a 1 in a stat is that you are using it as a dump stat to squeeze point for other things. Hence why GM's take a dim view of Dumpstat.
I'm currently in the process of making a Technomancer character who had some kind of matrix-accident, causing her to have lost all of her memories. She was then found by some curious sprites, who (in round-about fashion) helped her find her way to an ex-runner Technomancer they knew. He tried to get through to her, but she was traumatised in such a way that she was hard to talk to in the flesh, and evens cared of being there.
But she liked the sprites, causing her to spend almost all of her time in the matrix, and making her (re)education being virtually taken care of by the sprites, giving her a rather machine/AI like view on a lot of things.
I'll not get into how she ended up shadowrunning, but she operates out of a mecha with some drones. She basically hardly ever moves by herself (even in the mecha she's jumped in, so no cotnrols) so her physical body has suffered under that abuse. That is why she has 1 STR. Even if she gets out of the mech, she's supported by an Iron Will exoskeleton, so a lot of the movement isn't her own.
She pretty much can't dodge or do anything worth mentioning, combat-wise, outside of the mech. And seeing as the thing is quite big-ish, she'll have to get outside of it, lots, even if the GM isn't specifically out to force me to do so. Due to budget issues, she's not that great at hacking remotely either, or really hacking at all, so her use is being at the scene.
I think that's a "dumpstat" with real consequences, with good reasons and with RP implications.