Are you saying that some HIV positive individuals naturally develop these antibodies over time, curing themselves of HIV? Or am I misreading?
Your immune system can and does fight the HIV virus, it does loses that fight because HIV attacks the immune system, can hide for years, and has a cell to cell infection vector.
The immune system is also limited to what it can do, and when viruses can spread cell to cell there isn't much it can do since there is little to no attack surface available for the immune system to work with in that case.
Antibody and therapeutic vaccines can be used as post exposure treatments and combined with other regiments to help slow down or even control the progress of HIV and AIDS in already afflicted patients.
A therapeutic vaccine with a regiment of reverse-transcriptase inhibitors and a treatment to control cell suicide upon infection can probably be developed for HIV and for other retroviruses, well excluding the antibodies it is what we already are doing today mostly.
I am an absolute noob in science, but still want to ask out of curiosity. If a biological virus can have a cell to cell infection vector, can't an anti-body or immunogen also have a cell-to-cell "replenishing" factor?
An antibody is just a protein molecule with no ability to create copies of itself. It might move from one cell to another, but that does create a new synthesizer of the antibody at the new location, and so does not trigger a spread of the antibody throughout the tissue or organism.
Cell to call transfer and communication happens all the time, cells share nutrients and many other things, some viruses take advantage of that mechanism allowing them to basically cross cellular and tissue boundaries.
Some can exploit this to the extreme by actually replicating only parts of themselves in each cell and using the cell to cell transfer highway to be finally assembled in another cell, this is often used to prevent cell suicide since one of the intracellular defense mechanism is basically the cell invoking cell death upon detecting an infection.
If you want an analogy from the technology world think about it as staged payloads that some malware use, each payload on it's own is undetectable and even non-functional but when everything reaches the final target all the payloads are assembled into the final piece of malware that takes over the targeted host ;)
If you are interested in cell to cell infections NIH has an article about it
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3587356/
There are quite a few other sources on Google, overall viruses are pretty sneaky, some of them even ask the cell politely to establish new cell to cell contacts to facilitate cell to cell infection.
You might also like to look up virus assembly and budding, since it's also a pretty interesting topic, you might have viruses that do cell to cell infection of their naked forms then the final polymerization of their shells happens in another cell and they might even do the final budding in another.
Expect nightmares tho ;)
P.S.
Cell to cell transfers might also be called exocytosis (sometimes also called reversed endocytosis) (exit) and endocytosis (entry) so if you are googling and can't find what you need might need to use the scientific terms.
I see the comments about cell-to-cell infection; I don't know what it is about these controllers but it doesn't seem to be a problem for them.