Are there dildos (or vibrators?) that can be fully inserted and held inside someone?

One with a base will probably be your best bet. A little research on the anatomy of the vagina might not be remiss. The vagina is a dead end. Nothing can be "lost" inside of her.
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As you can see in this image, the vaginal tract ends at the cervix which is even smaller than it looks in this illustration. Medical instruments can be used to penetrate the cervix and the cervix dilates during labor to accomodate childbirth, but normally, the cervix is closed very tightly. In most women, a finger inserted can touch the tip of her cervix. It will feel like a button with a dip in the middle which is the opening, however it is too small to allow a finger to penetrate it, much less a dildo. Other than the cervix, the vagina is entirely closed.
More photos here: link
If something is fully inserted beyond the opening of her vagina, where no part of it remains outside, the object can easily be retrieved with fingers. For example, the string of a tampon may become pushed inside the vagina requiring the woman to reach inside with a finger to retrieve the string to allow for removal. Many women, similarly, use menstrual cups which sit inside the vagina. Most have no retrieval string so the woman simply reaches inside with one or two fingers and thumb to grip the base and remove it. Unlike the anus, objects cannot continue further into the body through the vagina.
There are plenty of toys, such as vaginal balls, that can be fully inserted. Some are equipped with a retrieval cord, not unlike a tampon, while others require the user or a partner to reach fingers inside to remove them. Most things that can be fully inserted will not require a rope or harness to hold it inside, however, as the pc muscle is fairly low in the vagina and will allow natural retention of most things of decent size once inserted above it, ie: menstrual cups and tampons, as well as vaginal kegel balls are retained by the pc muscle preventing them from slipping out. The concept of the strapless strap-on works similarly.
If you're looking for something to be fully inside her, something like kegel balls, ben wa balls, vaginal balls will work and not require a rope to hold it inside, her muscles will do that naturally. If you're looking for something for a rope or harness to hold, one with a base that remains outside of her will work best. Hope this helps.

With anything, especially BDSM, education and information is VITAL. i did not, by any means, intend to embarrass either of you, but better to be embarrassed and well informed and SAFE! For example, Shibari, and any other kind of bondage for that matter, CAN be dangerous if done improperly and requires an understanding of anatomy, nerves, muscular-skeletal system and circulation, in order to be done safely. If you're not already, especially if you're relatively inexperienced, i'd strongly recommend that you investigate BDSM groups in your area, many cities even have dedicated Shibari groups that meet for practice and demonstrations. Many online resources exist especially for Shibari, but nothing compares to hands-on experience and in-person instruction, especially for foundation knowledge! Trust me, even if you think your area doesn't have a group of kinky folks, they almost certainly do. They may be a little hidden but they exist and will welcome you with open arms. Many BDSM groups around the country and internationally (not sure where you are located) host meetings, discussion groups, workshops, classes, demonstrations and other events which can be very educational for new and experienced players alike. i promise that they are not scary or embarrassing in the least! my Mistress and i live a 24/7 D/s lifestyle and incorporate BDSM into Oour intimate play. Wwe are active in Oour local BDSM community and belong to a club in Oour area and regularly attend meetings and events as well as attending an annual weekend retreat which is heavily focussed on education and learning. You'll find, if you haven't yet, that the community is very warm, open and welcoming and almost universally eager to teach and share. Aside from many wonderful educational opportunities, being a part of the BDSM community will also afford you exposure to many different types of play which can be a far better, more realistic place to get inspiration and new ideas (and the education necessary to bring them to reality) than erotica. If you aren't able or willing to connect with a local community, then please be sure to educate yourselves with books and research (be careful what sources you trust!) and please be safe, sane, consensual and risk-aware! If i can be of any further help or advice, please feel free to inbox me. i don't mean to sound preachy or overbearing. i think BDSM is wonderful and encourage people to explore their kinks but i'm big proponent of safety and education as the best foundation for the hottest possible play.
For the purpose of your question, another poster recommended glass, which would be fine, but be mindful that glass is very rigid and will not move within her the way silicone will. There's nothing wrong with that but it depends on the effect you're going for to determine which material will be best. The decision will probably be between glass and silicone.
Also, yes, it is possible for items to be drawn up through the anus into the rectum and be unreachable, thus requiring medical intervention. In some cases, it is possible for the item to work it's own way out and be expelled through the natural processes of the body but, if it doesn't, it may become a blockage that will require medical intervention so it's strongly recommended that you never use any items anally that are not equipped with a firm base or handle that cannot be drawn into the body accidentally. This is, as i explained above, not a concern with vaginal insertion. Exploring her vagina with a finger will help you understand what the pictures i linked illustrate.
Good luck, and be safe!