It sounds like there are two questions here: what does it mean to be genderless, and how can I respond to those who think they are genderless.
So let's start from the beginning: Sex and gender refer to two separate things. Sex refers to one's biology, while gender refers to one's identity. For many, these two line up -- someone designated male at birth (sex) also identifies as male (gender). For many others, this is not the case. It's difficult to explain what this feels like, in part because feelings in general are difficult to explain, but also because different people can experience it differently. Assuming you know your gender, imagine if everyone you encountered insisted you were a different gender. They treated you according to the gender they insisted you are, regardless of what you told them, and wouldn't let you do things according to the gender you know you are. Pretty frustrating to have people assuming they know you better than you do, huh?
Being genderless is an identity for those who don't feel they align with any other gender, so whether they are treated as male, as female, or as any other gender, it just doesn't feel right. Not having any gender at all makes them feel much more comfortable and at ease. Every genderless person is unique, has gone through their own process to find their identity, and will go through their own process to present themselves as they are comfortable doing. Some genderless people may opt for hormone treatments and name changes, while others may not. The specifics of what it means to be genderless entirely depend on the individual.
Now, as for how to respond to someone asking if they are genderless... It's their identity, their decision. You can't choose for them, but you can support them as they figure it out. Reassure them that you support them no matter what, that they aren't broken or insane, that their feelings are valid. It doesn't matter if they were or were not abused in the past. It doesn't matter if they identified as a different gender previously, or if they identify as something else in the future. If they feel genderless, then they are. Your role as someone they have confided in is to accept, respect, and support them.