What happens if my companion hates me?
If I continually lose affection points with my companion, what happens? Does she run-away, drop dead, turn on me and fight to the death?
Solution 1:
UPDATE:
Apparently at some point, a patch has been applied to the game that now allows companions affection to be negative. See other answers for details. (I haven't confirmed this or I'd put the details in this answer.)
ORIGINAL:
No. Your companion's Affection can not go below the initial starting value, indicating neutral.
If you're on an RP server, feel free to role play their hatred towards you by staging a fight with them yourself, then never summoning them again after you betray them and let them die in a fight you tell them to start as you run away laughing at their demise.
Otherwise, (seriously) the benefit of having high Affection with a particular companion increases their chances of crafting and mission successes, yields better quality results and opens up better gear.
Solution 2:
I'm not sure what happens but if you get Khem Vhal mad, he will get a broken heart sign next to his affiliation. I'm not sure what that actually does but, he can start to go negative on you.
Solution 3:
You can in fact get a negative score. The heart will turn red and the number of negative points are indicated by a minus sign before the number.