There is congenital deafness in some Havanese lines, but it usually shows up really early. Did the vet say what might have caused it? The good news is that dogs adapt really well to being deaf.
There is definitely a difference between turning deaf and congenital deafness which is from birth. However, it's not unusual for people to miss the signs and the realize they're deaf when they're a bit older. This is especially true if they have unilateral deafness (one ear) or if they've been around a lot of other dogs where they can get cues from them Or even if they're in a space where the floors vibrate even slightly and they can pick up movement easily so act like they heard you approaching them.
There are some congenital deafness genes in Havanese though they don't seem to be as prevalent as they are in breeds like Dalmatians, boxers, australian shepherds, greyhounds, etc. In fact, when I was first looking to adopt the first thing I did look for was a deaf Havanese - I've had a lot of experience with deaf Dalmatians and so figured I would be the perfect adopter of a deaf havanese, but there didn't seem to be many. Of course, I don't know the Havanese club in the US's position on deafness - for example, the Dalmatian association has/ had (?) a position that any reputable breeder would put down a deaf one immediately. So, I don't know how reputable Havanese breeders would deal with a deaf one in their liter.
So, from my own experience (and contrary to some of the literature out there on deaf dogs that portray them as dangerous), dogs adapt very well to being deaf and are very trainable and are no more dangerous than other dogs with the right training. The only thing I did differently with my deaf dog(s) than I do with hearing ones is that I would desensitize them to being startled (this might sound controversial, but i did this by startling them all the time and then profusely treating and praising them until they weren't bothered at all when something startled them).
Other than that, the only big difference in training was that the first step was to get them to constantly check in with you and make sure they're looking at you so that they can see the signal. I did use a vibrating collar for mine (it was a custom made one that had 0 shock ability and only a light vibration to let her know I needed her attention) - or if I was somewhere with a softer floor I would stamp my foot. And then the only other thing is that you train with hand signals rather than words (but a lot of people train hearing dogs at higher levels that way too).
The easier part was that it was very easy to tell when she was just ignoring what you were telling her instead of whether she understood you or not. When Kelsey didn't want to listen she was really good at sliding her eyes past me when I was trying to get her attention OR even looking straight at me and then very deliberately moving her head to stare at the ceiling! lol.
I would adopt another deaf one in a heartbeat.