Is it Possible to learn social dances through YouTube?

Is it Possible to learn social dances through YouTube?
Is it possible to learn how to dance alone?

They were unable to afford classes, and were too shy to go to a group class.

It is possible to learn some things on YouTube but it will be extremely slow and inefficient. What you will not get is feedback on how well you are actually dancing. There is also an issue with learning social dancing alone. The main thing you need to learn when Social dancing is how to lead/follow. Having no partner is some problem, but having no teacher to spot and most importantly correct errors will make things very difficult.

Are you wanting to lead or follow?
My guess is it'll be harder to follow using youtube videos alone, since following relies on you sensing the lead's intention and the lead taking you through it.

you can only learn to really dance it if you work with a partner. If you just learn steps and go to a social, you won't have the connection to be able to dance with a partner. A teacher can give you corrections and feedback that you might not know you need when you try to learn things from a video.

At the end of the day, Social dances are partner dances.
You can't get far unless you dance with other people and take lessons.

But how you approach ballroom also depends on your personal goals. If dancing by yourself in your room to Waltz music is what would make you happy, then by all means, do that. If you want to become an adept social ballroom dancer, then you'll need to take group lessons and dance with various partners. If you want to become a competitive ballroom dancer (which is my personal goal & hobby), then you'll need to take private lessons, group lessons, and find a partner that you can dance with consistently.