I just want to clarify, by Unowned you mean not a personal girl?
If so, I spent a good portion of my SL Gor as "unowned" if that's what you mean. I've been owned by cities and houses and played city slave to coin girl and now again coin girl. I didn't mind it then and don't mind it now either, it's always worked pretty really well for me. In those times I've always had little interaction with the Slaver or owner and felt responsible to make my own RP.
I also played a personal slave and loved the story of that as well and found it comforting to log in and know you had guaranteed RP partner who you knew you meshed with and an going story you could just pick up without any set up, don't get me wrong I really did like that, but I don't have too many issues as a public slave either. Public slave gives me the freedom and the IC reason to interact with everyone and anyone. I tend to stand in my own way in RP and being a private slave I'd sometimes limit myself the types of interactions I'd do because it didn't make sense to me that as a private slave my girl would do certain things. Just my own personal pet peeve seeing private girls acting like public so I personally don't do it. So being public again I find I'm getting to do all kinds of RP that I hadn't in a while.
I feel like a cow because I don't want to sound like I'm bragging but I never lack for RP, sexual or otherwise, with all kinds of characters and types of roleplayers and almost none of my RP involves serving. I do realize every day that I'm ridiculously lucky, I have some sort of RP horseshoe stuck somewhere.
A couple of nights ago I was in the Tospit sweeping, was a quiet night, late and I was thinking about logging off. This stranger walks in and I admit for a moment I sighed thinking if only I'd logged out 5 minutes earlier I'd have been able to go to bed and now I'd have to least do a few posts and send him up to the village. So I smiled and dropped a little post, nothing special and waited... then BOOOM he dropped this wall of text double post emote on me. I could have fallen out of my chair. I ended up staying up all night rp'ing, and no, not sex, just this incredible scene that left me on the edge of my seat and his writing and vocabulary made me feel illiterate. The best writer I've ever met in SL in any genre bar none, and that's say a lot because I've played with a lot of incredible players.
Then he was gone and I don't know if I'll see him again as he doesn't play on that sim. For me the typist it was a one of scene, but for my Linx it had a serious impact on her and very much changed her story line and will be incorporated into what she does and where she goes from here.
If there is one downside of playing a public slave it's that there are more individual RP scenes than stories. I don't mind that either though because I feel the story is mine, my character's, and just like my life it's not made up of one person. I can weave the scenes I have with different people into the quilt that is her life, because even if some patches only show up once they were worth it. In the last two weeks I've had probably 6 amazing scenes with 6 different characters, about half of those did end up involving sexual RP. They might all have been one off's, but Linx's story still moves forward as HER story even if those characters never enter it again.
Edit to add... Technically the people who owned my character in those roles weren't NPC, they were players, but my stories never revolved around theirs and could go days or longer without ever seeing them even for a nod let alone a story shaping scene. Being part of a big house or kennel is very similar to being "unowned" in that way and if I can make these work I think I could make the NPC owner work just as well.