Class 2 is a special class of negative pronouns.
I do not know a linguistic term for this class (but I am sure there is one), but they are not "true negations", they express "lack of ability".

Not all the pronouns listed above can be used with this meaning. The "lack of ability" pronouns are: некого, нечего, негде, некуда, неоткуда, некогда, незачем and maybe some more.
What they actually express is that someone has no means (no time, no place, no reason) etc. to do something. The person is always in Dative.

Мне негде жить. - There is no place for me to live.
Ему негде работать. - There is no place (no room) for him to work.
Нам некуда бежать. - There is no place for us to run to.
Воде неоткуда течь. - There is no place for the water to flow from.
Мне некогда отдыхать. - There is no time for me to rest.
Сергею некогда учить английский. - There is no time for Sergey to learn English.
Тебе незачем туда ходить. - There is no reason for you to go there.
Анне незачем тебе помогать. - There is no reason for Anna to help you.

Note that "некого" and "нечего" are used as class 2 (lack of ability) only when they are in one of oblique cases (any case other than the dictionary form, i.e. any case other than just "некто" and "нечто"):
Мне некого просить о помощи. - There is nobody for me to ask for help.
Ему нечего ждать. - There is nothing for him to wait for.
Тебе некому писать письма. - There is nobody for you to write letters to.
Мне не к чему стремиться. - There is nothing for me to strive for (when there is a preposition, it is inserted between "не" and the root: к + нечему = не к чему).
Нам некем гордиться. - There is nobody for us to be proud of.
Джону нечем писать. - There is nothing for John to write with (he has nothing to write with).
Нам не о ком рассказывать. - There is nobody for us to tell stories about.
Нам не о чем разговаривать. - There is nothing for us to talk about.