might you consider those characters something along the lines of "retired"? they were still loved with attention put into them, but you've spent so much time with them that it's sorta exhausted all of your drive to plot and hc and whatnot for them? i don't think you'd need to give those characters away, especially if you're still attached somewhat, as they're still yours! it doesn't matter (imo) that they're not "actively" worked on, because you've already spent ten years with those characters and you don't need to kiss those 10 years away unless you don't want to.
answering the actual thread topic: yes, i do feel like some characters are like... i guess more of what you described: so much time and effort went into their stories that i don't really feel the drive to expand on them. but i don't really consider them "finished", in a sense? most of the time this happens with deep 'sona characters, as i like exploring their paths the most and they get a lot of art/writing/headcanoning done for them, and as i grow and change i sort of lose the vibe i retained, so they're shelved and replaced with different sonas who better match my needs in the moment.
but i don't think my old sonas are really finished? there are a lot of other stories i could write of them, relationships, drawings, etc. but i don't really want to work on them now (or possibly ever again)? i want to give them completed profiles at least so that they're nice and neat in my toyhouse, but actively writing for them seems out of the question. so i do sorta relate to what you're feeling. i just left them in my toyhouse - they're a part of me and were huge parts of my life, and i don't mind keeping them around out of nostalgia and appreciation for what they added to my life and relationships!