There are a lot of different types of poly relationship structures and different names for them. The base unit of relationship is a standard couple where 2 people are together. Add another person in and they can either be in a relationship with only one of those people and form a "hinge" aka "V" or be in a relationship with both of those people and form a "triad" aka "throuple". As many people as those involved consent to can be added this way.
Most of the time it's one person who is in a relationship with multiple people who are each in relationships with multiple people. This forms a "polycule". Where you have the people you're in relationships with aka your "paramours" and they have the people they're in relationships with aka your "metamours". This group of relationships can take many forms and can be drawn out into a cool diagram like a molecule, hence the name polycule.
The people you're in a relationship with can break up with you like in any other relationship and vice versa. It's more complicated when you add in housing situations if you're all living together, multiple people are all dating each other, or if two people are married.
Using one of my breakups as an example:
I've been in a triad where one person broke up with the other. I was then put in the middle of their breakup drama. I set a boundary of not wanting to deal with their drama/shit talking of the other. One of them kept breaking that boundary, so I broke up with that person while still being in a relationship with the other. Luckily I was living with the person I stayed with or that would've been way more complicated.