Faye lost a fight pretty badly once (well, technically she won--but at great consequence). As others have said, there's plenty of consequences both physical and emotional other than death. She lost her hand in the fight, and nearly lost her life. With doctors and healers on call, her wounds healed quickly enough and with no lingering problems... aside from her hand. Can't really do much about a severed hand. Due to the stress/injuries/fatigue, she was mostly unconscious for several days, and mostly bedridden for a week or two.
She was a little shaken by how close she'd come to dying, but it didn't really do any significant long-term damage, if only because it wasn't her first near-death experience and she's stubborn af. But she did have trouble coping with the facts that she'd gotten others who received serious injuries dragged into this fight, that it was her own father who took her hand and genuinely tried to kill her and come quite close to it, that she'd killed her father herself and the revenge didn't feel nearly as satisfying as she'd expected. On top of that, Val was struggling with his own issues of feeling useless after failing to save Faye from getting her hand sliced off and in her own sorry state Faye felt powerless to reassure him.
But most of all, she was affected by the absence of her hand. She saw it as the physical reminder of everything that had gone wrong (because of her) that day, on top of a handicap and physical deformity in general. She struggled to try to manage life with one hand and found herself torn between accepting help to make her life easier or turn it down out of pride. And, being more than a little vain, she worried about it making her unattractive. She didn't go out into public much while she was missing her hand and typically kept her arm clutched behind her back or otherwise hidden.
Eventually, she sought out a Magitek prosthetic which was a pretty fun little RP hook. She got her prosthetic hand, and now largely hides the fact she lost her hand and wears gloves pretty much 24/7. The hand took some getting used to as well, in order to not be clumsy or crush things with her robot hand--something pretty frustrating to someone who'd intentionally presented herself as elegant and dainty all her life.
tl;dr - There are a lot of physical and emotional consequences to losing a fight that can be played out to affect your character, long term or short term. To make them impactful, I'd recommend doing things that actually affect your RP habits like when and where you RP, or shape your character's interactions with people around them, or provide RP hooks of some sort to meet new people or start new storylines.
She was a little shaken by how close she'd come to dying, but it didn't really do any significant long-term damage, if only because it wasn't her first near-death experience and she's stubborn af. But she did have trouble coping with the facts that she'd gotten others who received serious injuries dragged into this fight, that it was her own father who took her hand and genuinely tried to kill her and come quite close to it, that she'd killed her father herself and the revenge didn't feel nearly as satisfying as she'd expected. On top of that, Val was struggling with his own issues of feeling useless after failing to save Faye from getting her hand sliced off and in her own sorry state Faye felt powerless to reassure him.
But most of all, she was affected by the absence of her hand. She saw it as the physical reminder of everything that had gone wrong (because of her) that day, on top of a handicap and physical deformity in general. She struggled to try to manage life with one hand and found herself torn between accepting help to make her life easier or turn it down out of pride. And, being more than a little vain, she worried about it making her unattractive. She didn't go out into public much while she was missing her hand and typically kept her arm clutched behind her back or otherwise hidden.
Eventually, she sought out a Magitek prosthetic which was a pretty fun little RP hook. She got her prosthetic hand, and now largely hides the fact she lost her hand and wears gloves pretty much 24/7. The hand took some getting used to as well, in order to not be clumsy or crush things with her robot hand--something pretty frustrating to someone who'd intentionally presented herself as elegant and dainty all her life.
tl;dr - There are a lot of physical and emotional consequences to losing a fight that can be played out to affect your character, long term or short term. To make them impactful, I'd recommend doing things that actually affect your RP habits like when and where you RP, or shape your character's interactions with people around them, or provide RP hooks of some sort to meet new people or start new storylines.