I'm not into amputees or anything involving abuse, but I imagine it is a more extreme form of BDSM. Quadruple amputation basically renders the subject/victim into a totally useless being, completely dependent on their "master" to a level similar to a baby's. Amputees can't move, feed, clean or defend themselves, so for a sadist person having somebody utterly dependent on you must bring a high form of pleasure. Similarly, making somebody a living fleshlight is an extreme form of objectification, even more than "merely" turning them into your servants or slaves. By crippling their movement you turn them into mere objects submitted to your will wherever they like it or not. Is an absolute form of control.
Finally, there's the "cute" aspect of it. Cute creatures that have suffered damage trigger a strong emotional response, and for some people the sight of a cute girl who has lost a limb or limbs must trigger such a response along with the typical sexual arousal that comes with the sight of a cute girl. The more benign amputee stories often show the victims as people who have lost the will to live but who gradually regain their spirit and happiness thanks to a person who decides to invest his or her time and resources in caring for them. This is an atypical form of romance that generates a stronger emotional response than the average story (since we are not used to thinking about people with amputations, much less how they might feel), and that may be what piques some people's interest the most.
In my case is the second approach. I have a fetish for cute and small beings and another one for fucking things that you normally wouldn't/shouldn't fuck, and lolis and shotas excel at satisfying both fetishes. They're much smaller than your average anime character, naturally cute thanks to their neotenous traits (rounder faces, softer skin, more fat deposits, innocence/ignorance, lack of explicitly sexual traits), and are literally build for having sex despite their small size. There's also the extreme taboo of them being (digital) children, which for some people (like me) only makes things more erotic because by engaging in lascivious acts with them you're breaking moral and legal norms. The trill of "breaking the norms" while fapping to loli/shota is really exciting, you're doing something most people don't do or want makes fapping to them much hotter than it would if lolicon and shotacon were completely normal.